id sid tid token lemma pos bjmsr-311 1 1 copyright copyright NOUN bjmsr-311 1 2 © © PROPN bjmsr-311 1 3 cc cc PROPN bjmsr-311 1 4 - - PUNCT bjmsr-311 1 5 by by ADP bjmsr-311 1 6 - - PUNCT bjmsr-311 1 7 nc nc PROPN bjmsr-311 1 8 2019 2019 NUM bjmsr-311 1 9 , , PUNCT bjmsr-311 1 10 bjmsr bjmsr PROPN bjmsr-311 1 11 bangladesh bangladesh PROPN bjmsr-311 1 12 journal journal PROPN bjmsr-311 1 13 of of ADP bjmsr-311 1 14 multidisciplinary multidisciplinary ADJ bjmsr-311 1 15 scientific scientific ADJ bjmsr-311 1 16 research research NOUN bjmsr-311 1 17 vol vol NOUN bjmsr-311 1 18 . . PROPN bjmsr-311 1 19 1 1 NUM bjmsr-311 1 20 , , PUNCT bjmsr-311 1 21 no no INTJ bjmsr-311 1 22 . . NOUN bjmsr-311 1 23 1 1 NUM bjmsr-311 1 24 april april PROPN bjmsr-311 1 25 - - PUNCT bjmsr-311 1 26 june june PROPN bjmsr-311 1 27 ; ; PUNCT bjmsr-311 1 28 2019 2019 NUM bjmsr-311 1 29 published publish VERB bjmsr-311 1 30 by by ADP bjmsr-311 1 31 centre centre NOUN bjmsr-311 1 32 for for ADP bjmsr-311 1 33 research research NOUN bjmsr-311 1 34 on on ADP bjmsr-311 1 35 islamic islamic ADJ bjmsr-311 1 36 banking banking PROPN bjmsr-311 1 37 & & CCONJ bjmsr-311 1 38 finance finance PROPN bjmsr-311 1 39 and and CCONJ bjmsr-311 1 40 business business NOUN bjmsr-311 1 41 1 1 NUM bjmsr-311 1 42 new new ADJ bjmsr-311 1 43 algorithms algorithm NOUN bjmsr-311 1 44 for for ADP bjmsr-311 1 45 l1 l1 PROPN bjmsr-311 1 46 norm norm PROPN bjmsr-311 1 47 regression regression PROPN bjmsr-311 1 48 bijan bijan PROPN bjmsr-311 1 49 bidabad bidabad PROPN bjmsr-311 1 50 b.a b.a PROPN bjmsr-311 1 51 . . PROPN bjmsr-311 1 52 , , PUNCT bjmsr-311 1 53 m.sc m.sc PROPN bjmsr-311 1 54 . . PROPN bjmsr-311 1 55 , , PUNCT bjmsr-311 1 56 ph.d ph.d PROPN bjmsr-311 1 57 . . PROPN bjmsr-311 1 58 , , PUNCT bjmsr-311 1 59 post post PROPN bjmsr-311 1 60 - - ADJ bjmsr-311 1 61 doc doc ADJ bjmsr-311 1 62 . . PROPN bjmsr-311 2 1 professor professor NOUN bjmsr-311 2 2 economics economic NOUN bjmsr-311 2 3 and and CCONJ bjmsr-311 2 4 chief chief ADJ bjmsr-311 2 5 islamic islamic PROPN bjmsr-311 2 6 banking banking PROPN bjmsr-311 2 7 advisor advisor PROPN bjmsr-311 2 8 bank bank PROPN bjmsr-311 2 9 melli melli PROPN bjmsr-311 2 10 , , PUNCT bjmsr-311 2 11 iran iran PROPN bjmsr-311 2 12 e-mail:bijan@bidabad.com e-mail:bijan@bidabad.com X bjmsr-311 3 1 abstract abstract ADJ bjmsr-311 3 2 in in ADP bjmsr-311 3 3 this this DET bjmsr-311 3 4 paper paper NOUN bjmsr-311 3 5 , , PUNCT bjmsr-311 3 6 we we PRON bjmsr-311 3 7 propose propose VERB bjmsr-311 3 8 four four NUM bjmsr-311 3 9 algorithms algorithm NOUN bjmsr-311 3 10 for for ADP bjmsr-311 3 11 l1 l1 PROPN bjmsr-311 3 12 norm norm NOUN bjmsr-311 3 13 computation computation NOUN bjmsr-311 3 14 of of ADP bjmsr-311 3 15 regression regression NOUN bjmsr-311 3 16 parameters parameter NOUN bjmsr-311 3 17 , , PUNCT bjmsr-311 3 18 where where SCONJ bjmsr-311 3 19 two two NUM bjmsr-311 3 20 of of ADP bjmsr-311 3 21 them they PRON bjmsr-311 3 22 are be AUX bjmsr-311 3 23 more more ADV bjmsr-311 3 24 efficient efficient ADJ bjmsr-311 3 25 for for ADP bjmsr-311 3 26 simple simple ADJ bjmsr-311 3 27 and and CCONJ bjmsr-311 3 28 multiple multiple ADJ bjmsr-311 3 29 regression regression NOUN bjmsr-311 3 30 models model NOUN bjmsr-311 3 31 . . PUNCT bjmsr-311 4 1 however however ADV bjmsr-311 4 2 , , PUNCT bjmsr-311 4 3 we we PRON bjmsr-311 4 4 start start VERB bjmsr-311 4 5 with with ADP bjmsr-311 4 6 restricted restricted ADJ bjmsr-311 4 7 simple simple ADJ bjmsr-311 4 8 linear linear ADJ bjmsr-311 4 9 regression regression NOUN bjmsr-311 4 10 and and CCONJ bjmsr-311 4 11 corresponding correspond VERB bjmsr-311 4 12 derivation derivation NOUN bjmsr-311 4 13 and and CCONJ bjmsr-311 4 14 computation computation NOUN bjmsr-311 4 15 of of ADP bjmsr-311 4 16 the the DET bjmsr-311 4 17 weighted weight VERB bjmsr-311 4 18 median median ADJ bjmsr-311 4 19 problem problem NOUN bjmsr-311 4 20 . . PUNCT bjmsr-311 5 1 in in ADP bjmsr-311 5 2 this this DET bjmsr-311 5 3 respect respect NOUN bjmsr-311 5 4 , , PUNCT bjmsr-311 5 5 a a DET bjmsr-311 5 6 computing computing NOUN bjmsr-311 5 7 function function NOUN bjmsr-311 5 8 is be AUX bjmsr-311 5 9 coded code VERB bjmsr-311 5 10 . . PUNCT bjmsr-311 6 1 with with ADP bjmsr-311 6 2 discussion discussion NOUN bjmsr-311 6 3 on on ADP bjmsr-311 6 4 the the DET bjmsr-311 6 5 m m PROPN bjmsr-311 6 6 parameters parameter NOUN bjmsr-311 6 7 model model NOUN bjmsr-311 6 8 , , PUNCT bjmsr-311 6 9 we we PRON bjmsr-311 6 10 continue continue VERB bjmsr-311 6 11 to to PART bjmsr-311 6 12 expand expand VERB bjmsr-311 6 13 the the DET bjmsr-311 6 14 algorithm algorithm NOUN bjmsr-311 6 15 to to PART bjmsr-311 6 16 include include VERB bjmsr-311 6 17 unrestricted unrestricted ADJ bjmsr-311 6 18 simple simple ADJ bjmsr-311 6 19 linear linear ADJ bjmsr-311 6 20 regression regression NOUN bjmsr-311 6 21 , , PUNCT bjmsr-311 6 22 and and CCONJ bjmsr-311 6 23 two two NUM bjmsr-311 6 24 crude crude ADJ bjmsr-311 6 25 and and CCONJ bjmsr-311 6 26 efficient efficient ADJ bjmsr-311 6 27 algorithms algorithm NOUN bjmsr-311 6 28 are be AUX bjmsr-311 6 29 proposed propose VERB bjmsr-311 6 30 . . PUNCT bjmsr-311 7 1 the the DET bjmsr-311 7 2 procedures procedure NOUN bjmsr-311 7 3 are be AUX bjmsr-311 7 4 then then ADV bjmsr-311 7 5 generalized generalize VERB bjmsr-311 7 6 to to ADP bjmsr-311 7 7 the the DET bjmsr-311 7 8 m m PROPN bjmsr-311 7 9 parameters parameter NOUN bjmsr-311 7 10 model model NOUN bjmsr-311 7 11 by by ADP bjmsr-311 7 12 presenting present VERB bjmsr-311 7 13 two two NUM bjmsr-311 7 14 new new ADJ bjmsr-311 7 15 algorithms algorithm NOUN bjmsr-311 7 16 , , PUNCT bjmsr-311 7 17 where where SCONJ bjmsr-311 7 18 the the DET bjmsr-311 7 19 algorithm algorithm NOUN bjmsr-311 7 20 4 4 NUM bjmsr-311 7 21 is be AUX bjmsr-311 7 22 selected select VERB bjmsr-311 7 23 as as ADP bjmsr-311 7 24 more more ADV bjmsr-311 7 25 efficient efficient ADJ bjmsr-311 7 26 . . PUNCT bjmsr-311 8 1 various various ADJ bjmsr-311 8 2 properties property NOUN bjmsr-311 8 3 of of ADP bjmsr-311 8 4 these these DET bjmsr-311 8 5 algorithms algorithm NOUN bjmsr-311 8 6 are be AUX bjmsr-311 8 7 discussed discuss VERB bjmsr-311 8 8 . . PUNCT bjmsr-311 9 1 keywords keyword NOUN bjmsr-311 9 2 : : PUNCT bjmsr-311 9 3 l1 l1 PROPN bjmsr-311 9 4 norm norm NOUN bjmsr-311 9 5 , , PUNCT bjmsr-311 9 6 regression regression NOUN bjmsr-311 9 7 , , PUNCT bjmsr-311 9 8 algorithm algorithm NOUN bjmsr-311 9 9 , , PUNCT bjmsr-311 9 10 computer computer NOUN bjmsr-311 9 11 program program NOUN bjmsr-311 9 12 1 1 NUM bjmsr-311 9 13 . . PUNCT bjmsr-311 9 14 introduction introduction NOUN bjmsr-311 9 15 in in ADP bjmsr-311 9 16 bidabad bidabad NOUN bjmsr-311 9 17 ( ( PUNCT bjmsr-311 9 18 1989a 1989a NUM bjmsr-311 9 19 , , PUNCT bjmsr-311 9 20 b b NOUN bjmsr-311 9 21 ) ) PUNCT bjmsr-311 9 22 , , PUNCT bjmsr-311 9 23 various various ADJ bjmsr-311 9 24 aspects aspect NOUN bjmsr-311 9 25 of of ADP bjmsr-311 9 26 the the DET bjmsr-311 9 27 l1 l1 PROPN bjmsr-311 9 28 norm norm NOUN bjmsr-311 9 29 regression regression NOUN bjmsr-311 9 30 were be AUX bjmsr-311 9 31 reviewed review VERB bjmsr-311 9 32 . . PUNCT bjmsr-311 10 1 we we PRON bjmsr-311 10 2 observed observe VERB bjmsr-311 10 3 that that SCONJ bjmsr-311 10 4 the the DET bjmsr-311 10 5 l1 l1 PROPN bjmsr-311 10 6 norm norm NOUN bjmsr-311 10 7 criterion criterion NOUN bjmsr-311 10 8 is be AUX bjmsr-311 10 9 going go VERB bjmsr-311 10 10 to to PART bjmsr-311 10 11 find find VERB bjmsr-311 10 12 its its PRON bjmsr-311 10 13 place place NOUN bjmsr-311 10 14 in in ADP bjmsr-311 10 15 scientific scientific ADJ bjmsr-311 10 16 analysis analysis NOUN bjmsr-311 10 17 . . PUNCT bjmsr-311 11 1 since since SCONJ bjmsr-311 11 2 it it PRON bjmsr-311 11 3 is be AUX bjmsr-311 11 4 not not PART bjmsr-311 11 5 computationally computationally ADV bjmsr-311 11 6 comparable comparable ADJ bjmsr-311 11 7 with with ADP bjmsr-311 11 8 other other ADJ bjmsr-311 11 9 criteria criterion NOUN bjmsr-311 11 10 such such ADJ bjmsr-311 11 11 as as ADP bjmsr-311 11 12 l2 l2 NOUN bjmsr-311 11 13 norm norm NOUN bjmsr-311 11 14 , , PUNCT bjmsr-311 11 15 it it PRON bjmsr-311 11 16 needs need VERB bjmsr-311 11 17 more more ADJ bjmsr-311 11 18 work work NOUN bjmsr-311 11 19 to to PART bjmsr-311 11 20 make make VERB bjmsr-311 11 21 it it PRON bjmsr-311 11 22 a a DET bjmsr-311 11 23 hand hand NOUN bjmsr-311 11 24 tool tool NOUN bjmsr-311 11 25 . . PUNCT bjmsr-311 12 1 the the DET bjmsr-311 12 2 closed closed ADJ bjmsr-311 12 3 form form NOUN bjmsr-311 12 4 of of ADP bjmsr-311 12 5 the the DET bjmsr-311 12 6 solution solution NOUN bjmsr-311 12 7 of of ADP bjmsr-311 12 8 the the DET bjmsr-311 12 9 l1 l1 PROPN bjmsr-311 12 10 norm norm NOUN bjmsr-311 12 11 estimator estimator NOUN bjmsr-311 12 12 has have AUX bjmsr-311 12 13 not not PART bjmsr-311 12 14 been be AUX bjmsr-311 12 15 derived derive VERB bjmsr-311 12 16 yet yet ADV bjmsr-311 12 17 , , PUNCT bjmsr-311 12 18 and and CCONJ bjmsr-311 12 19 therefore therefore ADV bjmsr-311 12 20 , , PUNCT bjmsr-311 12 21 makes make VERB bjmsr-311 12 22 further further ADJ bjmsr-311 12 23 inferences inference NOUN bjmsr-311 12 24 of of ADP bjmsr-311 12 25 the the DET bjmsr-311 12 26 properties property NOUN bjmsr-311 12 27 of of ADP bjmsr-311 12 28 this this DET bjmsr-311 12 29 estimator estimator NOUN bjmsr-311 12 30 difficult difficult ADJ bjmsr-311 12 31 . . PUNCT bjmsr-311 13 1 any any DET bjmsr-311 13 2 attempt attempt NOUN bjmsr-311 13 3 to to PART bjmsr-311 13 4 give give VERB bjmsr-311 13 5 efficient efficient ADJ bjmsr-311 13 6 computational computational ADJ bjmsr-311 13 7 algorithms algorithm NOUN bjmsr-311 13 8 which which PRON bjmsr-311 13 9 may may AUX bjmsr-311 13 10 introduce introduce VERB bjmsr-311 13 11 significant significant ADJ bjmsr-311 13 12 insight insight NOUN bjmsr-311 13 13 into into ADP bjmsr-311 13 14 the the DET bjmsr-311 13 15 different different ADJ bjmsr-311 13 16 characteristics characteristic NOUN bjmsr-311 13 17 of of ADP bjmsr-311 13 18 the the DET bjmsr-311 13 19 problem problem NOUN bjmsr-311 13 20 is be AUX bjmsr-311 13 21 desirable desirable ADJ bjmsr-311 13 22 . . PUNCT bjmsr-311 14 1 in in ADP bjmsr-311 14 2 this this DET bjmsr-311 14 3 regard regard NOUN bjmsr-311 14 4 , , PUNCT bjmsr-311 14 5 we we PRON bjmsr-311 14 6 shall shall AUX bjmsr-311 14 7 try try VERB bjmsr-311 14 8 to to PART bjmsr-311 14 9 give give VERB bjmsr-311 14 10 a a DET bjmsr-311 14 11 general general ADJ bjmsr-311 14 12 procedure procedure NOUN bjmsr-311 14 13 in in ADP bjmsr-311 14 14 this this DET bjmsr-311 14 15 paper paper NOUN bjmsr-311 14 16 to to PART bjmsr-311 14 17 solve solve VERB bjmsr-311 14 18 the the DET bjmsr-311 14 19 l1 l1 PROPN bjmsr-311 14 20 norm norm PROPN bjmsr-311 14 21 linear linear PROPN bjmsr-311 14 22 regression regression NOUN bjmsr-311 14 23 problem problem NOUN bjmsr-311 14 24 . . PUNCT bjmsr-311 15 1 the the DET bjmsr-311 15 2 proposed propose VERB bjmsr-311 15 3 algorithms algorithm NOUN bjmsr-311 15 4 are be AUX bjmsr-311 15 5 based base VERB bjmsr-311 15 6 on on ADP bjmsr-311 15 7 a a DET bjmsr-311 15 8 special special ADJ bjmsr-311 15 9 descent descent NOUN bjmsr-311 15 10 method method NOUN bjmsr-311 15 11 and and CCONJ bjmsr-311 15 12 use use VERB bjmsr-311 15 13 a a DET bjmsr-311 15 14 discrete discrete ADJ bjmsr-311 15 15 differentiation differentiation NOUN bjmsr-311 15 16 technique technique NOUN bjmsr-311 15 17 . . PUNCT bjmsr-311 16 1 primary primary ADJ bjmsr-311 16 2 designs design NOUN bjmsr-311 16 3 of of ADP bjmsr-311 16 4 the the DET bjmsr-311 16 5 algorithms algorithm NOUN bjmsr-311 16 6 have have AUX bjmsr-311 16 7 been be AUX bjmsr-311 16 8 discussed discuss VERB bjmsr-311 16 9 by by ADP bjmsr-311 16 10 bidabad bidabad NOUN bjmsr-311 16 11 ( ( PUNCT bjmsr-311 16 12 1987a 1987a NUM bjmsr-311 16 13 , , PUNCT bjmsr-311 16 14 b,88a b,88a ADJ bjmsr-311 16 15 , , PUNCT bjmsr-311 16 16 b b NOUN bjmsr-311 16 17 ) ) PUNCT bjmsr-311 16 18 . . PUNCT bjmsr-311 17 1 by by ADP bjmsr-311 17 2 manipulating manipulate VERB bjmsr-311 17 3 these these DET bjmsr-311 17 4 algorithms algorithm NOUN bjmsr-311 17 5 , , PUNCT bjmsr-311 17 6 more more ADV bjmsr-311 17 7 efficient efficient ADJ bjmsr-311 17 8 ones one NOUN bjmsr-311 17 9 were be AUX bjmsr-311 17 10 introduced introduce VERB bjmsr-311 17 11 by by ADP bjmsr-311 17 12 bidabad bidabad NOUN bjmsr-311 17 13 ( ( PUNCT bjmsr-311 17 14 1989a 1989a NUM bjmsr-311 17 15 , , PUNCT bjmsr-311 17 16 b b NOUN bjmsr-311 17 17 ) ) PUNCT bjmsr-311 17 18 which which PRON bjmsr-311 17 19 has have AUX bjmsr-311 17 20 been be AUX bjmsr-311 17 21 shown show VERB bjmsr-311 17 22 to to PART bjmsr-311 17 23 have have VERB bjmsr-311 17 24 better well ADJ bjmsr-311 17 25 performance performance NOUN bjmsr-311 17 26 than than ADP bjmsr-311 17 27 other other ADJ bjmsr-311 17 28 existing exist VERB bjmsr-311 17 29 algorithms algorithm NOUN bjmsr-311 17 30 . . PUNCT bjmsr-311 18 1 consider consider VERB bjmsr-311 18 2 the the DET bjmsr-311 18 3 following follow VERB bjmsr-311 18 4 regression regression NOUN bjmsr-311 18 5 model model NOUN bjmsr-311 18 6 , , PUNCT bjmsr-311 18 7 m m VERB bjmsr-311 18 8 yi yi NOUN bjmsr-311 18 9 = = PUNCT bjmsr-311 18 10   VERB bjmsr-311 18 11 jxji jxji NOUN bjmsr-311 18 12 + + CCONJ bjmsr-311 18 13 ui ui PROPN bjmsr-311 18 14 i=1, i=1, PROPN bjmsr-311 18 15 ... ... PUNCT bjmsr-311 18 16 ,n ,n PUNCT bjmsr-311 18 17 ( ( PUNCT bjmsr-311 18 18 1 1 X bjmsr-311 18 19 ) ) PUNCT bjmsr-311 18 20 j=1 j=1 NOUN bjmsr-311 18 21 where where SCONJ bjmsr-311 18 22 j j NOUN bjmsr-311 18 23 , , PUNCT bjmsr-311 18 24 j=1, j=1, NOUN bjmsr-311 18 25 ... ... PUNCT bjmsr-311 18 26 ,m ,m PUNCT bjmsr-311 18 27 are be AUX bjmsr-311 18 28 population population NOUN bjmsr-311 18 29 parameters parameter NOUN bjmsr-311 18 30 to to PART bjmsr-311 18 31 be be AUX bjmsr-311 18 32 estimated estimate VERB bjmsr-311 18 33 , , PUNCT bjmsr-311 18 34 yi yi PROPN bjmsr-311 18 35 , , PUNCT bjmsr-311 18 36 xji xji PROPN bjmsr-311 18 37 and and CCONJ bjmsr-311 18 38 ui ui PROPN bjmsr-311 18 39 are be AUX bjmsr-311 18 40 dependent dependent ADJ bjmsr-311 18 41 , , PUNCT bjmsr-311 18 42 independent independent ADJ bjmsr-311 18 43 , , PUNCT bjmsr-311 18 44 and and CCONJ bjmsr-311 18 45 random random ADJ bjmsr-311 18 46 variables variable NOUN bjmsr-311 18 47 respectively respectively ADV bjmsr-311 18 48 . . PUNCT bjmsr-311 19 1 we we PRON bjmsr-311 19 2 wish wish VERB bjmsr-311 19 3 to to PART bjmsr-311 19 4 estimate estimate VERB bjmsr-311 19 5 j j NOUN bjmsr-311 19 6 's 's PART bjmsr-311 19 7 by by ADP bjmsr-311 19 8 minimizing minimize VERB bjmsr-311 19 9 the the DET bjmsr-311 19 10 expression expression NOUN bjmsr-311 19 11 , , PUNCT bjmsr-311 19 12 n n CCONJ bjmsr-311 19 13 n n PRON bjmsr-311 19 14 m m NOUN bjmsr-311 19 15 s s PART bjmsr-311 19 16 = = X bjmsr-311 19 17   ADJ bjmsr-311 19 18 │ │ ADJ bjmsr-311 19 19 ui^ ui^ NOUN bjmsr-311 19 20 │ │ NOUN bjmsr-311 19 21 = = SYM bjmsr-311 19 22   ADP bjmsr-311 19 23 │ │ ADJ bjmsr-311 19 24 yi yi NOUN bjmsr-311 19 25   ADP bjmsr-311 19 26 ßj^xji ßj^xji NOUN bjmsr-311 19 27 │ │ PUNCT bjmsr-311 19 28 ( ( PUNCT bjmsr-311 19 29 2 2 NUM bjmsr-311 19 30 ) ) PUNCT bjmsr-311 19 31 i=1 i=1 PROPN bjmsr-311 19 32 i=1 i=1 PROPN bjmsr-311 20 1 j=1 j=1 PROPN bjmsr-311 20 2 suppose suppose VERB bjmsr-311 20 3 m=1 m=1 NOUN bjmsr-311 20 4 , , PUNCT bjmsr-311 20 5 then then ADV bjmsr-311 20 6 expression expression NOUN bjmsr-311 20 7 ( ( PUNCT bjmsr-311 20 8 2 2 X bjmsr-311 20 9 ) ) PUNCT bjmsr-311 20 10 reduces reduce VERB bjmsr-311 20 11 to to ADP bjmsr-311 20 12 , , PUNCT bjmsr-311 20 13 n n CCONJ bjmsr-311 20 14 n n CCONJ bjmsr-311 20 15 n n NOUN bjmsr-311 20 16 s s NOUN bjmsr-311 20 17 = = X bjmsr-311 20 18   ADJ bjmsr-311 20 19 │ │ NOUN bjmsr-311 20 20 yi yi NOUN bjmsr-311 20 21 yi^ yi^ ADJ bjmsr-311 20 22 │ │ ADV bjmsr-311 20 23 = = SYM bjmsr-311 20 24   ADP bjmsr-311 20 25 │ │ NUM bjmsr-311 20 26 yi yi NOUN bjmsr-311 20 27 ß^xi ß^xi NOUN bjmsr-311 20 28 │ │ PUNCT bjmsr-311 20 29 = = PUNCT bjmsr-311 20 30   X bjmsr-311 20 31 si si X bjmsr-311 20 32 ( ( PUNCT bjmsr-311 20 33 3 3 NUM bjmsr-311 20 34 ) ) PUNCT bjmsr-311 20 35 i=1 i=1 VERB bjmsr-311 20 36 i=1 i=1 X bjmsr-311 21 1 i=1 i=1 PROPN bjmsr-311 21 2 a a DET bjmsr-311 21 3 typical typical ADJ bjmsr-311 21 4 element element NOUN bjmsr-311 21 5 , , PUNCT bjmsr-311 21 6 si=|yi-^xi| si=|yi-^xi| PROPN bjmsr-311 21 7 can can AUX bjmsr-311 21 8 be be AUX bjmsr-311 21 9 viewed view VERB bjmsr-311 21 10 as as ADP bjmsr-311 21 11 a a DET bjmsr-311 21 12 broken broken ADJ bjmsr-311 21 13 line line NOUN bjmsr-311 21 14 in in ADP bjmsr-311 21 15 the the DET bjmsr-311 21 16 sx^ sx^ NOUN bjmsr-311 21 17 plane plane NOUN bjmsr-311 21 18 composed compose VERB bjmsr-311 21 19 of of ADP bjmsr-311 21 20 two two NUM bjmsr-311 21 21 half half ADJ bjmsr-311 21 22 - - PUNCT bjmsr-311 21 23 lines line NOUN bjmsr-311 21 24 . . PUNCT bjmsr-311 22 1 si si PROPN bjmsr-311 22 2 attains attain VERB bjmsr-311 22 3 its its PRON bjmsr-311 22 4 minimum minimum NOUN bjmsr-311 22 5 which which PRON bjmsr-311 22 6 is be AUX bjmsr-311 22 7 zero zero NUM bjmsr-311 22 8 at at ADP bjmsr-311 22 9 , , PUNCT bjmsr-311 22 10 mailto:bijan@bidabad.com mailto:bijan@bidabad.com PROPN bjmsr-311 22 11 copyright copyright PROPN bjmsr-311 23 1 © © PROPN bjmsr-311 23 2 cc cc PROPN bjmsr-311 23 3 - - PUNCT bjmsr-311 23 4 by by ADP bjmsr-311 23 5 - - PUNCT bjmsr-311 23 6 nc nc PROPN bjmsr-311 23 7 2019 2019 NUM bjmsr-311 23 8 , , PUNCT bjmsr-311 23 9 bjmsr bjmsr PROPN bjmsr-311 23 10 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 23 11 bangladesh bangladesh PROPN bjmsr-311 23 12 journal journal PROPN bjmsr-311 23 13 of of ADP bjmsr-311 23 14 multidisciplinary multidisciplinary ADJ bjmsr-311 23 15 scientific scientific ADJ bjmsr-311 23 16 research research NOUN bjmsr-311 23 17 vol vol NOUN bjmsr-311 23 18 . . PROPN bjmsr-311 24 1 1 1 NUM bjmsr-311 24 2 , , PUNCT bjmsr-311 24 3 no no INTJ bjmsr-311 24 4 . . NOUN bjmsr-311 24 5 1 1 NUM bjmsr-311 24 6 ; ; PUNCT bjmsr-311 24 7 2019 2019 NUM bjmsr-311 24 8 2 2 NUM bjmsr-311 24 9 i^ i^ NOUN bjmsr-311 24 10 = = SYM bjmsr-311 24 11 yi yi PROPN bjmsr-311 24 12 / / SYM bjmsr-311 24 13 xi xi X bjmsr-311 24 14 ( ( PUNCT bjmsr-311 24 15 4 4 X bjmsr-311 24 16 ) ) PUNCT bjmsr-311 24 17 the the DET bjmsr-311 24 18 slopes slope NOUN bjmsr-311 24 19 of of ADP bjmsr-311 24 20 the the DET bjmsr-311 24 21 half half ADJ bjmsr-311 24 22 - - PUNCT bjmsr-311 24 23 lines line NOUN bjmsr-311 24 24 to to ADP bjmsr-311 24 25 the the DET bjmsr-311 24 26 left left NOUN bjmsr-311 24 27 and and CCONJ bjmsr-311 24 28 right right NOUN bjmsr-311 24 29 of of ADP bjmsr-311 24 30 i^ i^ PROPN bjmsr-311 24 31 are be AUX bjmsr-311 24 32 -|xi| -|xi| ADJ bjmsr-311 24 33 and and CCONJ bjmsr-311 24 34 |xi| |xi| PROPN bjmsr-311 24 35 respectively respectively ADV bjmsr-311 24 36 . . PUNCT bjmsr-311 25 1 so so ADV bjmsr-311 25 2 , , PUNCT bjmsr-311 25 3 si si PROPN bjmsr-311 25 4 's 's PART bjmsr-311 25 5 are be AUX bjmsr-311 25 6 all all PRON bjmsr-311 25 7 convex convex ADJ bjmsr-311 25 8 , , PUNCT bjmsr-311 25 9 and and CCONJ bjmsr-311 25 10 hence hence ADV bjmsr-311 25 11 their their PRON bjmsr-311 25 12 sum sum NOUN bjmsr-311 25 13 s s VERB bjmsr-311 25 14 is be AUX bjmsr-311 25 15 also also ADV bjmsr-311 25 16 convex convex ADJ bjmsr-311 25 17 with with ADP bjmsr-311 25 18 a a DET bjmsr-311 25 19 slope slope NOUN bjmsr-311 25 20 at at ADP bjmsr-311 25 21 any any DET bjmsr-311 25 22 ^ ^ PROPN bjmsr-311 25 23 equal equal ADJ bjmsr-311 25 24 to to ADP bjmsr-311 25 25 the the DET bjmsr-311 25 26 sum sum NOUN bjmsr-311 25 27 of of ADP bjmsr-311 25 28 the the DET bjmsr-311 25 29 slopes slope NOUN bjmsr-311 25 30 of of ADP bjmsr-311 25 31 si si NOUN bjmsr-311 25 32 's 's PART bjmsr-311 25 33 at at ADP bjmsr-311 25 34 that that DET bjmsr-311 25 35 value value NOUN bjmsr-311 25 36 of of ADP bjmsr-311 25 37 ^. ^. PROPN bjmsr-311 25 38 since since SCONJ bjmsr-311 25 39 the the DET bjmsr-311 25 40 slope slope NOUN bjmsr-311 25 41 of of ADP bjmsr-311 25 42 each each DET bjmsr-311 25 43 si si NOUN bjmsr-311 25 44 changes change NOUN bjmsr-311 25 45 only only ADV bjmsr-311 25 46 at at ADP bjmsr-311 25 47 the the DET bjmsr-311 25 48 corresponding corresponding ADJ bjmsr-311 25 49 i^ i^ PROPN bjmsr-311 25 50 , , PUNCT bjmsr-311 25 51 the the DET bjmsr-311 25 52 minimum minimum NOUN bjmsr-311 25 53 of of ADP bjmsr-311 25 54 s s PRON bjmsr-311 25 55 will will AUX bjmsr-311 25 56 lie lie VERB bjmsr-311 25 57 on on ADP bjmsr-311 25 58 one one NUM bjmsr-311 25 59 of of ADP bjmsr-311 25 60 the the DET bjmsr-311 25 61 i^. i^. PROPN bjmsr-311 25 62 thus thus ADV bjmsr-311 25 63 , , PUNCT bjmsr-311 25 64 the the DET bjmsr-311 25 65 regression regression NOUN bjmsr-311 25 66 line line NOUN bjmsr-311 25 67 will will AUX bjmsr-311 25 68 pass pass VERB bjmsr-311 25 69 through through ADP bjmsr-311 25 70 origin origin NOUN bjmsr-311 25 71 with with ADP bjmsr-311 25 72 the the DET bjmsr-311 25 73 slope slope NOUN bjmsr-311 25 74 equal equal ADJ bjmsr-311 25 75 to to ADP bjmsr-311 25 76 i^ i^ NUM bjmsr-311 25 77 which which PRON bjmsr-311 25 78 minimizes minimize VERB bjmsr-311 25 79 s. s. PROPN bjmsr-311 25 80 on on ADP bjmsr-311 25 81 the the DET bjmsr-311 25 82 other other ADJ bjmsr-311 25 83 hand hand NOUN bjmsr-311 25 84 , , PUNCT bjmsr-311 25 85 to to PART bjmsr-311 25 86 find find VERB bjmsr-311 25 87 the the DET bjmsr-311 25 88 l1 l1 PROPN bjmsr-311 25 89 norm norm NOUN bjmsr-311 25 90 estimate estimate NOUN bjmsr-311 25 91 of of ADP bjmsr-311 25 92   NOUN bjmsr-311 25 93 we we PRON bjmsr-311 25 94 need need VERB bjmsr-311 25 95 to to PART bjmsr-311 25 96 find find VERB bjmsr-311 25 97 only only ADV bjmsr-311 25 98 one one NUM bjmsr-311 25 99 observation observation NOUN bjmsr-311 25 100 ( ( PUNCT bjmsr-311 25 101 see see VERB bjmsr-311 25 102 , , PUNCT bjmsr-311 25 103 karst karst PROPN bjmsr-311 25 104 ( ( PUNCT bjmsr-311 25 105 1958 1958 NUM bjmsr-311 25 106 ) ) PUNCT bjmsr-311 25 107 , , PUNCT bjmsr-311 25 108 taylor taylor PROPN bjmsr-311 25 109 ( ( PUNCT bjmsr-311 25 110 1974 1974 NUM bjmsr-311 25 111 ) ) PUNCT bjmsr-311 25 112 ) ) PUNCT bjmsr-311 25 113 . . PUNCT bjmsr-311 26 1 furthermore furthermore ADV bjmsr-311 26 2 , , PUNCT bjmsr-311 26 3 taylor taylor PROPN bjmsr-311 26 4 ( ( PUNCT bjmsr-311 26 5 1974 1974 NUM bjmsr-311 26 6 ) ) PUNCT bjmsr-311 26 7 concludes conclude VERB bjmsr-311 26 8 that that SCONJ bjmsr-311 26 9 : : PUNCT bjmsr-311 26 10 " " PUNCT bjmsr-311 26 11 this this PRON bjmsr-311 26 12 implies imply VERB bjmsr-311 26 13 , , PUNCT bjmsr-311 26 14 of of ADP bjmsr-311 26 15 course course NOUN bjmsr-311 26 16 , , PUNCT bjmsr-311 26 17 that that SCONJ bjmsr-311 26 18 the the DET bjmsr-311 26 19 regression regression NOUN bjmsr-311 26 20 line line NOUN bjmsr-311 26 21 must must AUX bjmsr-311 26 22 pass pass VERB bjmsr-311 26 23 through through ADP bjmsr-311 26 24 the the DET bjmsr-311 26 25 observation observation NOUN bjmsr-311 26 26 corresponding correspond VERB bjmsr-311 26 27 to to ADP bjmsr-311 26 28 the the DET bjmsr-311 26 29 minimizing minimizing NOUN bjmsr-311 26 30 i. i. NOUN bjmsr-311 26 31 the the DET bjmsr-311 26 32 regression regression NOUN bjmsr-311 26 33 line line NOUN bjmsr-311 26 34 , , PUNCT bjmsr-311 26 35 therefore therefore ADV bjmsr-311 26 36 , , PUNCT bjmsr-311 26 37 is be AUX bjmsr-311 26 38 determined determine VERB bjmsr-311 26 39 by by ADP bjmsr-311 26 40 the the DET bjmsr-311 26 41 point point NOUN bjmsr-311 26 42 of of ADP bjmsr-311 26 43 origin origin NOUN bjmsr-311 26 44 and and CCONJ bjmsr-311 26 45 the the DET bjmsr-311 26 46 observation observation NOUN bjmsr-311 26 47 associated associate VERB bjmsr-311 26 48 with with ADP bjmsr-311 26 49 minimizing minimize VERB bjmsr-311 26 50 i^ i^ NOUN bjmsr-311 26 51 " " PUNCT bjmsr-311 26 52 . . PUNCT bjmsr-311 27 1 but but CCONJ bjmsr-311 27 2 he he PRON bjmsr-311 27 3 did do AUX bjmsr-311 27 4 not not PART bjmsr-311 27 5 continue continue VERB bjmsr-311 27 6 this this DET bjmsr-311 27 7 approach approach NOUN bjmsr-311 27 8 , , PUNCT bjmsr-311 27 9 that that ADV bjmsr-311 27 10 is is ADV bjmsr-311 27 11 , , PUNCT bjmsr-311 27 12 minimizing minimize VERB bjmsr-311 27 13 s s PRON bjmsr-311 27 14 with with ADP bjmsr-311 27 15 respect respect NOUN bjmsr-311 27 16 to to ADP bjmsr-311 27 17 subscript subscript VERB bjmsr-311 27 18 i. i. NOUN bjmsr-311 27 19 in in ADP bjmsr-311 27 20 this this DET bjmsr-311 27 21 paper paper NOUN bjmsr-311 27 22 as as ADP bjmsr-311 27 23 bidabad bidabad NOUN bjmsr-311 27 24 ( ( PUNCT bjmsr-311 27 25 1987a,88a 1987a,88a NUM bjmsr-311 27 26 ) ) PUNCT bjmsr-311 27 27 a a DET bjmsr-311 27 28 first first ADJ bjmsr-311 27 29 endeavor endeavor NOUN bjmsr-311 27 30 is be AUX bjmsr-311 27 31 to to PART bjmsr-311 27 32 develop develop VERB bjmsr-311 27 33 this this DET bjmsr-311 27 34 point point NOUN bjmsr-311 27 35 of of ADP bjmsr-311 27 36 view view NOUN bjmsr-311 27 37 . . PUNCT bjmsr-311 28 1 in in ADP bjmsr-311 28 2 the the DET bjmsr-311 28 3 next next ADJ bjmsr-311 28 4 section section NOUN bjmsr-311 28 5 , , PUNCT bjmsr-311 28 6 after after ADP bjmsr-311 28 7 rewriting rewrite VERB bjmsr-311 28 8 ( ( PUNCT bjmsr-311 28 9 3 3 NUM bjmsr-311 28 10 ) ) PUNCT bjmsr-311 28 11 in in ADP bjmsr-311 28 12 a a DET bjmsr-311 28 13 suitable suitable ADJ bjmsr-311 28 14 fashion fashion NOUN bjmsr-311 28 15 , , PUNCT bjmsr-311 28 16 the the DET bjmsr-311 28 17 value value NOUN bjmsr-311 28 18 of of ADP bjmsr-311 28 19 i i PRON bjmsr-311 28 20 is be AUX bjmsr-311 28 21 determined determine VERB bjmsr-311 28 22 by by ADP bjmsr-311 28 23 using use VERB bjmsr-311 28 24 discrete discrete ADJ bjmsr-311 28 25 differentiation differentiation NOUN bjmsr-311 28 26 . . PUNCT bjmsr-311 29 1 by by ADP bjmsr-311 29 2 a a DET bjmsr-311 29 3 similar similar ADJ bjmsr-311 29 4 discussion discussion NOUN bjmsr-311 29 5 , , PUNCT bjmsr-311 29 6 it it PRON bjmsr-311 29 7 can can AUX bjmsr-311 29 8 be be AUX bjmsr-311 29 9 concluded conclude VERB bjmsr-311 29 10 that that SCONJ bjmsr-311 29 11 when when SCONJ bjmsr-311 29 12 the the DET bjmsr-311 29 13 number number NOUN bjmsr-311 29 14 of of ADP bjmsr-311 29 15 parameters parameter NOUN bjmsr-311 29 16 is be AUX bjmsr-311 29 17 m m PROPN bjmsr-311 29 18 , , PUNCT bjmsr-311 29 19 m m VERB bjmsr-311 29 20 observations observation NOUN bjmsr-311 29 21 must must AUX bjmsr-311 29 22 lie lie VERB bjmsr-311 29 23 on on ADP bjmsr-311 29 24 the the DET bjmsr-311 29 25 regression regression NOUN bjmsr-311 29 26 hyperplane hyperplane NOUN bjmsr-311 29 27 . . PUNCT bjmsr-311 30 1 on on ADP bjmsr-311 30 2 the the DET bjmsr-311 30 3 other other ADJ bjmsr-311 30 4 hand hand NOUN bjmsr-311 30 5 , , PUNCT bjmsr-311 30 6 m m NOUN bjmsr-311 30 7 equations equation NOUN bjmsr-311 30 8 of of ADP bjmsr-311 30 9 the the DET bjmsr-311 30 10 form form NOUN bjmsr-311 30 11 given give VERB bjmsr-311 30 12 by by ADP bjmsr-311 30 13 ( ( PUNCT bjmsr-311 30 14 5 5 NUM bjmsr-311 30 15 ) ) PUNCT bjmsr-311 30 16 are be AUX bjmsr-311 30 17 necessary necessary ADJ bjmsr-311 30 18 to to PART bjmsr-311 30 19 specify specify VERB bjmsr-311 30 20 the the DET bjmsr-311 30 21 regression regression NOUN bjmsr-311 30 22 hyperplane hyperplane NOUN bjmsr-311 30 23 ( ( PUNCT bjmsr-311 30 24 see see VERB bjmsr-311 30 25 also also ADV bjmsr-311 30 26 bidabad bidabad VERB bjmsr-311 30 27 ( ( PUNCT bjmsr-311 30 28 1989a 1989a NUM bjmsr-311 30 29 , , PUNCT bjmsr-311 30 30 b b NOUN bjmsr-311 30 31 ) ) PUNCT bjmsr-311 30 32 ) ) PUNCT bjmsr-311 30 33 . . PUNCT bjmsr-311 31 1 m m VERB bjmsr-311 31 2 yi yi PROPN bjmsr-311 31 3   VERB bjmsr-311 31 4 j^xji j^xji NOUN bjmsr-311 31 5 = = SYM bjmsr-311 31 6 0 0 NUM bjmsr-311 31 7 ( ( PUNCT bjmsr-311 31 8 5 5 NUM bjmsr-311 31 9 ) ) PUNCT bjmsr-311 31 10 j=1 j=1 NOUN bjmsr-311 31 11 now now ADV bjmsr-311 31 12 , , PUNCT bjmsr-311 31 13 let let VERB bjmsr-311 31 14 us we PRON bjmsr-311 31 15 proceed proceed VERB bjmsr-311 31 16 with with ADP bjmsr-311 31 17 the the DET bjmsr-311 31 18 simplest simple ADJ bjmsr-311 31 19 regression regression NOUN bjmsr-311 31 20 model model NOUN bjmsr-311 31 21 . . PUNCT bjmsr-311 32 1 2 2 X bjmsr-311 32 2 . . NUM bjmsr-311 32 3 restricted restrict VERB bjmsr-311 32 4 simple simple ADJ bjmsr-311 32 5 linear linear ADJ bjmsr-311 32 6 regression regression NOUN bjmsr-311 32 7 for for ADP bjmsr-311 32 8 model model NOUN bjmsr-311 32 9 ( ( PUNCT bjmsr-311 32 10 1 1 X bjmsr-311 32 11 ) ) PUNCT bjmsr-311 32 12 consider consider VERB bjmsr-311 32 13 the the DET bjmsr-311 32 14 case case NOUN bjmsr-311 32 15 of of ADP bjmsr-311 32 16 one one NUM bjmsr-311 32 17 independent independent ADJ bjmsr-311 32 18 variable variable NOUN bjmsr-311 32 19 with with ADP bjmsr-311 32 20 no no DET bjmsr-311 32 21 intercept intercept NOUN bjmsr-311 32 22 , , PUNCT bjmsr-311 32 23 namely namely ADV bjmsr-311 32 24 , , PUNCT bjmsr-311 32 25 y y PROPN bjmsr-311 32 26 i=xi+ui i=xi+ui NOUN bjmsr-311 32 27 . . PUNCT bjmsr-311 33 1 to to PART bjmsr-311 33 2 find find VERB bjmsr-311 33 3 the the DET bjmsr-311 33 4 l1 l1 PROPN bjmsr-311 33 5 norm norm NOUN bjmsr-311 33 6 estimate estimate NOUN bjmsr-311 33 7 of of ADP bjmsr-311 33 8   PROPN bjmsr-311 33 9 , , PUNCT bjmsr-311 33 10 the the DET bjmsr-311 33 11 following follow VERB bjmsr-311 33 12 procedure procedure NOUN bjmsr-311 33 13 can can AUX bjmsr-311 33 14 be be AUX bjmsr-311 33 15 suggested suggest VERB bjmsr-311 33 16 . . PUNCT bjmsr-311 34 1 n n CCONJ bjmsr-311 34 2 n n CCONJ bjmsr-311 34 3 n n CCONJ bjmsr-311 34 4 n n NOUN bjmsr-311 34 5 s s NOUN bjmsr-311 34 6 = = PUNCT bjmsr-311 34 7   NOUN bjmsr-311 34 8 |ui| |ui| PROPN bjmsr-311 34 9 = = PUNCT bjmsr-311 34 10   NOUN bjmsr-311 34 11 |yi |yi NUM bjmsr-311 34 12 xi| xi| NOUN bjmsr-311 34 13 = = SYM bjmsr-311 34 14   ADJ bjmsr-311 34 15 ( ( PUNCT bjmsr-311 34 16 yi yi NOUN bjmsr-311 34 17 xi)sgn(yi xi)sgn(yi ADV bjmsr-311 34 18 xi xi NOUN bjmsr-311 34 19 ) ) PUNCT bjmsr-311 34 20 = = PUNCT bjmsr-311 35 1   ADP bjmsr-311 35 2 |xi|(yi |xi|(yi NOUN bjmsr-311 35 3 / / SYM bjmsr-311 35 4 xi xi X bjmsr-311 35 5 )sgn(yi )sgn(yi PROPN bjmsr-311 35 6 / / SYM bjmsr-311 35 7 xi xi PROPN bjmsr-311 35 8   PROPN bjmsr-311 35 9 ) ) PUNCT bjmsr-311 35 10 ( ( PUNCT bjmsr-311 35 11 6 6 NUM bjmsr-311 35 12 ) ) PUNCT bjmsr-311 36 1 i=1 i=1 VERB bjmsr-311 36 2 i=1 i=1 X bjmsr-311 37 1 i=1 i=1 X bjmsr-311 38 1 i=1 i=1 PROPN bjmsr-311 38 2 let let VERB bjmsr-311 38 3 zi zi PRON bjmsr-311 38 4 = = VERB bjmsr-311 38 5 yi yi PROPN bjmsr-311 38 6 / / SYM bjmsr-311 38 7 xi xi PROPN bjmsr-311 38 8 and and CCONJ bjmsr-311 38 9 sort sort ADV bjmsr-311 38 10 zi zi NOUN bjmsr-311 38 11 in in ADP bjmsr-311 38 12 descending descend VERB bjmsr-311 38 13 order order NOUN bjmsr-311 38 14 . . PUNCT bjmsr-311 39 1 rename rename VERB bjmsr-311 39 2 the the DET bjmsr-311 39 3 resultant resultant NOUN bjmsr-311 39 4 ordered order VERB bjmsr-311 39 5 zi zi PROPN bjmsr-311 39 6 , , PUNCT bjmsr-311 39 7 i=1, i=1, PROPN bjmsr-311 39 8 ... ... PUNCT bjmsr-311 39 9 ,n ,n PUNCT bjmsr-311 39 10 to to ADP bjmsr-311 39 11 zh zh PROPN bjmsr-311 39 12 , , PUNCT bjmsr-311 39 13 h=1, h=1, PROPN bjmsr-311 39 14 ... ... PUNCT bjmsr-311 39 15 ,n ,n NOUN bjmsr-311 39 16 . . PUNCT bjmsr-311 40 1 elements element NOUN bjmsr-311 40 2 of of ADP bjmsr-311 40 3 zh zh PROPN bjmsr-311 40 4 should should AUX bjmsr-311 40 5 have have VERB bjmsr-311 40 6 the the DET bjmsr-311 40 7 following follow VERB bjmsr-311 40 8 property property NOUN bjmsr-311 40 9 : : PUNCT bjmsr-311 40 10 zh zh X bjmsr-311 40 11 > > X bjmsr-311 40 12 zl zl PROPN bjmsr-311 40 13 if if SCONJ bjmsr-311 40 14 h h PRON bjmsr-311 40 15 < < X bjmsr-311 40 16 l l NOUN bjmsr-311 40 17 for for ADP bjmsr-311 40 18 all all DET bjmsr-311 40 19 h h NOUN bjmsr-311 40 20 , , PUNCT bjmsr-311 40 21 l=1, l=1, NOUN bjmsr-311 40 22 ... ... PUNCT bjmsr-311 40 23 ,n ,n PUNCT bjmsr-311 40 24 . . PUNCT bjmsr-311 41 1 rewrite rewrite PROPN bjmsr-311 41 2 ( ( PUNCT bjmsr-311 41 3 6 6 NUM bjmsr-311 41 4 ) ) PUNCT bjmsr-311 41 5 with with ADP bjmsr-311 41 6 ordered order VERB bjmsr-311 41 7 observations observation NOUN bjmsr-311 41 8 as as ADP bjmsr-311 41 9 , , PUNCT bjmsr-311 41 10 n n PROPN bjmsr-311 41 11 s s NOUN bjmsr-311 41 12 = = PUNCT bjmsr-311 41 13   X bjmsr-311 41 14 |xh|(zh |xh|(zh NUM bjmsr-311 41 15 )sgn(zh- )sgn(zh- PROPN bjmsr-311 41 16 ) ) PUNCT bjmsr-311 41 17 ( ( PUNCT bjmsr-311 41 18 7 7 X bjmsr-311 41 19 ) ) PUNCT bjmsr-311 41 20 h=1 h=1 AUX bjmsr-311 41 21 let let VERB bjmsr-311 41 22 us we PRON bjmsr-311 41 23 denote denote VERB bjmsr-311 41 24 the the DET bjmsr-311 41 25 observation observation NOUN bjmsr-311 41 26 which which PRON bjmsr-311 41 27 will will AUX bjmsr-311 41 28 be be AUX bjmsr-311 41 29 on on ADP bjmsr-311 41 30 the the DET bjmsr-311 41 31 regression regression NOUN bjmsr-311 41 32 line line NOUN bjmsr-311 41 33 by by ADP bjmsr-311 41 34 ( ( PUNCT bjmsr-311 41 35 xt+1,yt+1 xt+1,yt+1 PROPN bjmsr-311 41 36 ) ) PUNCT bjmsr-311 41 37 that that PRON bjmsr-311 41 38 is be AUX bjmsr-311 41 39 the the DET bjmsr-311 41 40 ( ( PUNCT bjmsr-311 41 41 t+1)th t+1)th NOUN bjmsr-311 41 42 observation observation NOUN bjmsr-311 41 43 in in ADP bjmsr-311 41 44 the the DET bjmsr-311 41 45 zh zh PROPN bjmsr-311 41 46 array array NOUN bjmsr-311 41 47 . . PUNCT bjmsr-311 42 1 value value NOUN bjmsr-311 42 2 of of ADP bjmsr-311 42 3 zh zh PROPN bjmsr-311 42 4 is be AUX bjmsr-311 42 5 the the DET bjmsr-311 42 6 slope slope NOUN bjmsr-311 42 7 of of ADP bjmsr-311 42 8 a a DET bjmsr-311 42 9 ray ray NOUN bjmsr-311 42 10 passing pass VERB bjmsr-311 42 11 through through ADP bjmsr-311 42 12 the the DET bjmsr-311 42 13 origin origin NOUN bjmsr-311 42 14 and and CCONJ bjmsr-311 42 15 the the DET bjmsr-311 42 16 hth hth PROPN bjmsr-311 42 17 observation observation NOUN bjmsr-311 42 18 . . PUNCT bjmsr-311 43 1 therefore therefore ADV bjmsr-311 43 2 , , PUNCT bjmsr-311 43 3 if if SCONJ bjmsr-311 43 4 , , PUNCT bjmsr-311 43 5 h h NOUN bjmsr-311 43 6 < < X bjmsr-311 43 7 t+1 t+1 X bjmsr-311 43 8 then then ADV bjmsr-311 43 9 , , PUNCT bjmsr-311 43 10 zh zh INTJ bjmsr-311 43 11 > > X bjmsr-311 43 12   PROPN bjmsr-311 43 13 and and CCONJ bjmsr-311 43 14 uh uh INTJ bjmsr-311 43 15 > > X bjmsr-311 43 16 0 0 PUNCT bjmsr-311 44 1 if if SCONJ bjmsr-311 44 2 , , PUNCT bjmsr-311 44 3 h h NOUN bjmsr-311 44 4 = = NOUN bjmsr-311 44 5 t+1 t+1 PROPN bjmsr-311 44 6 then then ADV bjmsr-311 44 7 , , PUNCT bjmsr-311 44 8 zh zh PROPN bjmsr-311 44 9 = = SYM bjmsr-311 44 10   PROPN bjmsr-311 44 11 and and CCONJ bjmsr-311 44 12 uh uh INTJ bjmsr-311 44 13 = = SYM bjmsr-311 44 14 0 0 PUNCT bjmsr-311 44 15 if if SCONJ bjmsr-311 44 16 , , PUNCT bjmsr-311 44 17 h h NOUN bjmsr-311 44 18 > > X bjmsr-311 44 19 t+1 t+1 PROPN bjmsr-311 44 20 then then ADV bjmsr-311 44 21 , , PUNCT bjmsr-311 44 22 zh zh INTJ bjmsr-311 44 23 < < X bjmsr-311 44 24   NOUN bjmsr-311 44 25 and and CCONJ bjmsr-311 44 26 uh uh INTJ bjmsr-311 44 27 < < X bjmsr-311 44 28 0 0 NUM bjmsr-311 44 29 we we PRON bjmsr-311 44 30 can can AUX bjmsr-311 44 31 now now ADV bjmsr-311 44 32 rewrite rewrite VERB bjmsr-311 44 33 ( ( PUNCT bjmsr-311 44 34 7 7 NUM bjmsr-311 44 35 ) ) PUNCT bjmsr-311 44 36 as as SCONJ bjmsr-311 44 37 follows follow VERB bjmsr-311 44 38 , , PUNCT bjmsr-311 44 39 t t PROPN bjmsr-311 44 40 n n NOUN bjmsr-311 44 41 s s PART bjmsr-311 44 42 = = X bjmsr-311 44 43   ADJ bjmsr-311 44 44 |xh|(zh |xh|(zh NUM bjmsr-311 44 45   PROPN bjmsr-311 44 46 ) ) PUNCT bjmsr-311 44 47   VERB bjmsr-311 44 48 |xh|(zh |xh|(zh NUM bjmsr-311 44 49   PROPN bjmsr-311 44 50 ) ) PUNCT bjmsr-311 44 51 ( ( PUNCT bjmsr-311 44 52 8) 8) NUM bjmsr-311 44 53 h=1 h=1 NOUN bjmsr-311 44 54 h h NOUN bjmsr-311 44 55 = = NOUN bjmsr-311 44 56 t+1 t+1 X bjmsr-311 44 57 to to PART bjmsr-311 44 58 find find VERB bjmsr-311 44 59 the the DET bjmsr-311 44 60 minimum minimum NOUN bjmsr-311 44 61 of of ADP bjmsr-311 44 62 s s PROPN bjmsr-311 44 63 , , PUNCT bjmsr-311 44 64 we we PRON bjmsr-311 44 65 need need VERB bjmsr-311 44 66 to to PART bjmsr-311 44 67 differentiate differentiate VERB bjmsr-311 44 68 it it PRON bjmsr-311 44 69 with with ADP bjmsr-311 44 70 respect respect NOUN bjmsr-311 44 71 to to ADP bjmsr-311 44 72   NOUN bjmsr-311 44 73 and and CCONJ bjmsr-311 44 74 subscript subscript PROPN bjmsr-311 44 75 t t PROPN bjmsr-311 44 76 , , PUNCT bjmsr-311 44 77 because because SCONJ bjmsr-311 44 78 both both PRON bjmsr-311 44 79   PROPN bjmsr-311 44 80 and and CCONJ bjmsr-311 44 81 t t PROPN bjmsr-311 44 82 are be AUX bjmsr-311 44 83 unknowns unknown NOUN bjmsr-311 44 84 . . PUNCT bjmsr-311 45 1 note note VERB bjmsr-311 45 2 that that SCONJ bjmsr-311 45 3   PROPN bjmsr-311 45 4 has have VERB bjmsr-311 45 5 continuous continuous ADJ bjmsr-311 45 6 domain domain NOUN bjmsr-311 45 7 and and CCONJ bjmsr-311 45 8 t t NOUN bjmsr-311 45 9 has have VERB bjmsr-311 45 10 discrete discrete ADJ bjmsr-311 45 11 domain domain NOUN bjmsr-311 45 12 . . PUNCT bjmsr-311 46 1 thus thus ADV bjmsr-311 46 2 , , PUNCT bjmsr-311 46 3 δs δs ADP bjmsr-311 46 4 t t PROPN bjmsr-311 46 5 n n CCONJ bjmsr-311 46 6 ─ ─ PROPN bjmsr-311 46 7 ─ ─ PROPN bjmsr-311 46 8 = = PUNCT bjmsr-311 46 9   PROPN bjmsr-311 46 10 │ │ ADJ bjmsr-311 46 11 xh xh PROPN bjmsr-311 46 12 │ │ X bjmsr-311 46 13 + + CCONJ bjmsr-311 46 14   VERB bjmsr-311 46 15 │ │ ADJ bjmsr-311 46 16 xh xh PROPN bjmsr-311 46 17 │ │ X bjmsr-311 46 18 ( ( PUNCT bjmsr-311 46 19 9 9 NUM bjmsr-311 46 20 ) ) PUNCT bjmsr-311 46 21 δß δß ADP bjmsr-311 46 22 h=1 h=1 NOUN bjmsr-311 46 23 h h NOUN bjmsr-311 46 24 = = NOUN bjmsr-311 46 25 t+1 t+1 X bjmsr-311 46 26 the the DET bjmsr-311 46 27 differentiation differentiation NOUN bjmsr-311 46 28 of of ADP bjmsr-311 46 29 s s PRON bjmsr-311 46 30 with with ADP bjmsr-311 46 31 respect respect NOUN bjmsr-311 46 32 to to PART bjmsr-311 46 33 subscript subscript NOUN bjmsr-311 46 34 t t PROPN bjmsr-311 46 35 must must AUX bjmsr-311 46 36 be be AUX bjmsr-311 46 37 discrete discrete ADJ bjmsr-311 46 38 derivative derivative ADJ bjmsr-311 46 39 ( ( PUNCT bjmsr-311 46 40 see see NOUN bjmsr-311 46 41 , , PUNCT bjmsr-311 46 42 bender bender NOUN bjmsr-311 46 43 and and CCONJ bjmsr-311 46 44 orszag orszag NOUN bjmsr-311 46 45 ( ( PUNCT bjmsr-311 46 46 1978 1978 NUM bjmsr-311 46 47 ) ) PUNCT bjmsr-311 46 48 , , PUNCT bjmsr-311 46 49 clarke clarke PROPN bjmsr-311 46 50 ( ( PUNCT bjmsr-311 46 51 1983 1983 NUM bjmsr-311 46 52 ) ) PUNCT bjmsr-311 46 53 ): ): PUNCT bjmsr-311 46 54 (s (s NOUN bjmsr-311 46 55 ) ) PUNCT bjmsr-311 46 56 s[t+(t)]-s(t s[t+(t)]-s(t VERB bjmsr-311 46 57 ) ) PUNCT bjmsr-311 46 58 ─ ─ ADJ bjmsr-311 46 59 ─ ─ X bjmsr-311 46 60 ─ ─ PROPN bjmsr-311 46 61 = = SYM bjmsr-311 46 62 lim lim PROPN bjmsr-311 46 63 ─ ─ PROPN bjmsr-311 46 64 ─ ─ PROPN bjmsr-311 46 65 ─ ─ PROPN bjmsr-311 46 66 ─ ─ ADJ bjmsr-311 46 67 ─ ─ ADJ bjmsr-311 46 68 ─ ─ ADJ bjmsr-311 46 69 ─ ─ ADJ bjmsr-311 46 70 ─ ─ ADJ bjmsr-311 46 71 ─ ─ PROPN bjmsr-311 46 72 ─ ─ PROPN bjmsr-311 46 73 = = SYM bjmsr-311 46 74 s(t+1)-s(t s(t+1)-s(t PROPN bjmsr-311 46 75 ) ) PUNCT bjmsr-311 46 76 = = NOUN bjmsr-311 47 1 copyright copyright NOUN bjmsr-311 47 2 © © PROPN bjmsr-311 47 3 cc cc PROPN bjmsr-311 47 4 - - PUNCT bjmsr-311 47 5 by by ADP bjmsr-311 47 6 - - PUNCT bjmsr-311 47 7 nc nc PROPN bjmsr-311 47 8 2019 2019 NUM bjmsr-311 47 9 , , PUNCT bjmsr-311 47 10 bjmsr bjmsr PROPN bjmsr-311 47 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 47 12 bangladesh bangladesh PROPN bjmsr-311 47 13 journal journal PROPN bjmsr-311 47 14 of of ADP bjmsr-311 47 15 multidisciplinary multidisciplinary ADJ bjmsr-311 47 16 scientific scientific ADJ bjmsr-311 47 17 research research NOUN bjmsr-311 47 18 vol vol NOUN bjmsr-311 47 19 . . PROPN bjmsr-311 47 20 1 1 NUM bjmsr-311 47 21 , , PUNCT bjmsr-311 47 22 no no INTJ bjmsr-311 47 23 . . NOUN bjmsr-311 47 24 1 1 NUM bjmsr-311 47 25 ; ; PUNCT bjmsr-311 47 26 2019 2019 NUM bjmsr-311 47 27 3 3 NUM bjmsr-311 47 28 (t (t PROPN bjmsr-311 47 29 ) ) PUNCT bjmsr-311 47 30 (t) (t) PROPN bjmsr-311 47 31 ─ ─ PROPN bjmsr-311 47 32 >1 >1 NOUN bjmsr-311 47 33 (t (t PROPN bjmsr-311 47 34 ) ) PUNCT bjmsr-311 47 35 t+1 t+1 PROPN bjmsr-311 47 36 n n PART bjmsr-311 47 37 t t PROPN bjmsr-311 47 38 n n ADV bjmsr-311 47 39   VERB bjmsr-311 47 40 │ │ NUM bjmsr-311 47 41 xh xh NOUN bjmsr-311 47 42 │ │ ADJ bjmsr-311 47 43 (zh (zh NOUN bjmsr-311 47 44 - - PUNCT bjmsr-311 47 45 ß ß NOUN bjmsr-311 47 46 ) ) PUNCT bjmsr-311 47 47   ADJ bjmsr-311 47 48 │ │ NOUN bjmsr-311 47 49 xh xh PROPN bjmsr-311 47 50 │ │ ADJ bjmsr-311 47 51 (zh (zh NOUN bjmsr-311 47 52 - - PUNCT bjmsr-311 47 53 ß ß NOUN bjmsr-311 47 54 ) ) PUNCT bjmsr-311 47 55   ADJ bjmsr-311 47 56 │ │ NOUN bjmsr-311 47 57 xh xh PROPN bjmsr-311 47 58 │ │ ADJ bjmsr-311 47 59 (zh (zh NOUN bjmsr-311 47 60 - - PUNCT bjmsr-311 47 61 ß ß NOUN bjmsr-311 47 62 ) ) PUNCT bjmsr-311 47 63 + + CCONJ bjmsr-311 47 64   VERB bjmsr-311 47 65 │ │ NUM bjmsr-311 47 66 xh xh NOUN bjmsr-311 47 67 │ │ ADJ bjmsr-311 47 68 (zh (zh NOUN bjmsr-311 47 69 - - PUNCT bjmsr-311 47 70 ß ß NOUN bjmsr-311 47 71 ) ) PUNCT bjmsr-311 47 72 = = SYM bjmsr-311 47 73 2 2 NUM bjmsr-311 47 74 │ │ NUM bjmsr-311 47 75 xt+1 xt+1 NUM bjmsr-311 47 76 │ │ ADJ bjmsr-311 47 77 (zt+1 (zt+1 PROPN bjmsr-311 47 78 - - PUNCT bjmsr-311 47 79 ß ß NOUN bjmsr-311 47 80 ) ) PUNCT bjmsr-311 47 81 = = SYM bjmsr-311 47 82 0 0 NUM bjmsr-311 48 1 h=1 h=1 NOUN bjmsr-311 48 2 h h NOUN bjmsr-311 48 3 = = NOUN bjmsr-311 49 1 t+2 t+2 PRON bjmsr-311 49 2 h=1 h=1 NOUN bjmsr-311 49 3 h h NOUN bjmsr-311 49 4 = = NOUN bjmsr-311 49 5 t+1 t+1 X bjmsr-311 49 6 thus thus ADV bjmsr-311 49 7 , , PUNCT bjmsr-311 49 8 ß^ ß^ X bjmsr-311 49 9 = = SYM bjmsr-311 49 10 zt+1 zt+1 PROPN bjmsr-311 49 11 = = PUNCT bjmsr-311 49 12 yt+1 yt+1 PROPN bjmsr-311 49 13 / / SYM bjmsr-311 49 14 xt+1 xt+1 PROPN bjmsr-311 49 15 ( ( PUNCT bjmsr-311 49 16 10 10 NUM bjmsr-311 49 17 ) ) PUNCT bjmsr-311 49 18 it it PRON bjmsr-311 49 19 should should AUX bjmsr-311 49 20 be be AUX bjmsr-311 49 21 noted note VERB bjmsr-311 49 22 that that SCONJ bjmsr-311 49 23 if if SCONJ bjmsr-311 49 24 xt+1=0 xt+1=0 ADP bjmsr-311 49 25 then then ADV bjmsr-311 49 26 the the DET bjmsr-311 49 27 value value NOUN bjmsr-311 49 28 of of ADP bjmsr-311 49 29 zt+1 zt+1 PROPN bjmsr-311 49 30 = = PROPN bjmsr-311 49 31 l l NOUN bjmsr-311 49 32 , , PUNCT bjmsr-311 49 33 and and CCONJ bjmsr-311 49 34 when when SCONJ bjmsr-311 49 35 the the DET bjmsr-311 49 36 array array NOUN bjmsr-311 49 37 z z NOUN bjmsr-311 49 38 is be AUX bjmsr-311 49 39 sorted sort VERB bjmsr-311 49 40 , , PUNCT bjmsr-311 49 41 infinite infinite ADJ bjmsr-311 49 42 values value NOUN bjmsr-311 49 43 of of ADP bjmsr-311 49 44 z z NOUN bjmsr-311 49 45 locate locate NOUN bjmsr-311 49 46 at at ADP bjmsr-311 49 47 extremes extreme NOUN bjmsr-311 49 48 of of ADP bjmsr-311 49 49 two two NUM bjmsr-311 49 50 tails tail NOUN bjmsr-311 49 51 of of ADP bjmsr-311 49 52 the the DET bjmsr-311 49 53 array array NOUN bjmsr-311 49 54 and and CCONJ bjmsr-311 49 55 make make VERB bjmsr-311 49 56 no no DET bjmsr-311 49 57 problem problem NOUN bjmsr-311 49 58 in in ADP bjmsr-311 49 59 ( ( PUNCT bjmsr-311 49 60 10 10 NUM bjmsr-311 49 61 ) ) PUNCT bjmsr-311 49 62 . . PUNCT bjmsr-311 50 1 remember remember VERB bjmsr-311 50 2 that that PRON bjmsr-311 50 3 equation equation NOUN bjmsr-311 50 4 ( ( PUNCT bjmsr-311 50 5 10 10 NUM bjmsr-311 50 6 ) ) PUNCT bjmsr-311 50 7 is be AUX bjmsr-311 50 8 the the DET bjmsr-311 50 9 same same ADJ bjmsr-311 50 10 as as ADP bjmsr-311 50 11 relation relation NOUN bjmsr-311 50 12 ( ( PUNCT bjmsr-311 50 13 4 4 NUM bjmsr-311 50 14 ) ) PUNCT bjmsr-311 50 15 . . PUNCT bjmsr-311 51 1 equations equation NOUN bjmsr-311 51 2 ( ( PUNCT bjmsr-311 51 3 9 9 NUM bjmsr-311 51 4 ) ) PUNCT bjmsr-311 51 5 and and CCONJ bjmsr-311 51 6 ( ( PUNCT bjmsr-311 51 7 10 10 NUM bjmsr-311 51 8 ) ) PUNCT bjmsr-311 51 9 are be AUX bjmsr-311 51 10 two two NUM bjmsr-311 51 11 equations equation NOUN bjmsr-311 51 12 with with ADP bjmsr-311 51 13 two two NUM bjmsr-311 51 14 unknowns unknown NOUN bjmsr-311 51 15 t t PROPN bjmsr-311 51 16 and and CCONJ bjmsr-311 51 17 . . ADV bjmsr-311 51 18 the the DET bjmsr-311 51 19 variable variable ADJ bjmsr-311 51 20 t t PROPN bjmsr-311 51 21 can can AUX bjmsr-311 51 22 be be AUX bjmsr-311 51 23 found find VERB bjmsr-311 51 24 by by ADP bjmsr-311 51 25 rewriting rewrite VERB bjmsr-311 51 26 ( ( PUNCT bjmsr-311 51 27 9 9 NUM bjmsr-311 51 28 ) ) PUNCT bjmsr-311 51 29 as as SCONJ bjmsr-311 51 30 follows follow VERB bjmsr-311 51 31 , , PUNCT bjmsr-311 51 32 k k PROPN bjmsr-311 51 33 n n CCONJ bjmsr-311 51 34 dk dk PROPN bjmsr-311 51 35 ≡ ≡ PROPN bjmsr-311 51 36   VERB bjmsr-311 51 37 │ │ NUM bjmsr-311 51 38 xh xh PROPN bjmsr-311 51 39 │ │ X bjmsr-311 51 40   VERB bjmsr-311 51 41 │ │ ADJ bjmsr-311 51 42 xh xh PROPN bjmsr-311 51 43 │ │ ADJ bjmsr-311 51 44 k=1, k=1, NOUN bjmsr-311 51 45 ... ... PUNCT bjmsr-311 51 46 ,n ,n PUNCT bjmsr-311 51 47 ( ( PUNCT bjmsr-311 51 48 11 11 NUM bjmsr-311 51 49 ) ) PUNCT bjmsr-311 51 50 h=1 h=1 NOUN bjmsr-311 51 51 h h NOUN bjmsr-311 51 52 = = VERB bjmsr-311 51 53 k+1 k+1 X bjmsr-311 51 54 it it PRON bjmsr-311 51 55 is be AUX bjmsr-311 51 56 obvious obvious ADJ bjmsr-311 51 57 that that SCONJ bjmsr-311 51 58 dk dk PROPN bjmsr-311 51 59 is be AUX bjmsr-311 51 60 an an DET bjmsr-311 51 61 increasing increase VERB bjmsr-311 51 62 function function NOUN bjmsr-311 51 63 of of ADP bjmsr-311 51 64 k. k. PROPN bjmsr-311 51 65 when when SCONJ bjmsr-311 51 66 k k PROPN bjmsr-311 51 67 increases increase VERB bjmsr-311 51 68 from from ADP bjmsr-311 51 69 one one NUM bjmsr-311 51 70 to to ADP bjmsr-311 51 71 n n CCONJ bjmsr-311 51 72 , , PUNCT bjmsr-311 51 73 dk dk PROPN bjmsr-311 51 74 attains attain VERB bjmsr-311 51 75 different different ADJ bjmsr-311 51 76 values value NOUN bjmsr-311 51 77 , , PUNCT bjmsr-311 51 78 which which PRON bjmsr-311 51 79 increase increase VERB bjmsr-311 51 80 from from ADP bjmsr-311 51 81 negative negative ADJ bjmsr-311 51 82 to to ADP bjmsr-311 51 83 positive positive ADJ bjmsr-311 51 84 . . PUNCT bjmsr-311 52 1 so so ADV bjmsr-311 52 2 , , PUNCT bjmsr-311 52 3 initially initially ADV bjmsr-311 52 4 , , PUNCT bjmsr-311 52 5 k k PROPN bjmsr-311 52 6 is be AUX bjmsr-311 52 7 set set VERB bjmsr-311 52 8 equal equal ADJ bjmsr-311 52 9 to to ADP bjmsr-311 52 10 one one NUM bjmsr-311 52 11 , , PUNCT bjmsr-311 52 12 and and CCONJ bjmsr-311 52 13 dk dk PROPN bjmsr-311 52 14 is be AUX bjmsr-311 52 15 computed compute VERB bjmsr-311 52 16 accordingly accordingly ADV bjmsr-311 52 17 . . PUNCT bjmsr-311 53 1 if if SCONJ bjmsr-311 53 2 dk dk PROPN bjmsr-311 53 3 is be AUX bjmsr-311 53 4 negative negative ADJ bjmsr-311 53 5 , , PUNCT bjmsr-311 53 6 k k PROPN bjmsr-311 53 7 is be AUX bjmsr-311 53 8 increased increase VERB bjmsr-311 53 9 by by ADP bjmsr-311 53 10 one one NUM bjmsr-311 53 11 , , PUNCT bjmsr-311 53 12 and and CCONJ bjmsr-311 53 13 the the DET bjmsr-311 53 14 procedure procedure NOUN bjmsr-311 53 15 is be AUX bjmsr-311 53 16 repeated repeat VERB bjmsr-311 53 17 until until SCONJ bjmsr-311 53 18 dk dk PROPN bjmsr-311 53 19 becomes become VERB bjmsr-311 53 20 positive positive ADJ bjmsr-311 53 21 . . PUNCT bjmsr-311 54 1 when when SCONJ bjmsr-311 54 2 dk dk PROPN bjmsr-311 54 3 reaches reach VERB bjmsr-311 54 4 the the DET bjmsr-311 54 5 first first ADJ bjmsr-311 54 6 positive positive ADJ bjmsr-311 54 7 value value NOUN bjmsr-311 54 8 , , PUNCT bjmsr-311 54 9 then then ADV bjmsr-311 54 10 , , PUNCT bjmsr-311 54 11 t+1 t+1 PROPN bjmsr-311 54 12 = = PROPN bjmsr-311 54 13 k. k. PROPN bjmsr-311 54 14 by by ADP bjmsr-311 54 15 this this DET bjmsr-311 54 16 procedure procedure NOUN bjmsr-311 54 17 , , PUNCT bjmsr-311 54 18 the the DET bjmsr-311 54 19 value value NOUN bjmsr-311 54 20 of of ADP bjmsr-311 54 21 t+1 t+1 PROPN bjmsr-311 54 22 is be AUX bjmsr-311 54 23 found find VERB bjmsr-311 54 24 . . PUNCT bjmsr-311 55 1 the the DET bjmsr-311 55 2 observation observation NOUN bjmsr-311 55 3 corresponding correspond VERB bjmsr-311 55 4 to to ADP bjmsr-311 55 5 this this DET bjmsr-311 55 6 subscript subscript NOUN bjmsr-311 55 7 ( ( PUNCT bjmsr-311 55 8 t+1 t+1 PROPN bjmsr-311 55 9 = = PROPN bjmsr-311 55 10 k k NOUN bjmsr-311 55 11 ) ) PUNCT bjmsr-311 55 12 is be AUX bjmsr-311 55 13 selected select VERB bjmsr-311 55 14 ( ( PUNCT bjmsr-311 55 15 xt+1,yt+1 xt+1,yt+1 PROPN bjmsr-311 55 16 ) ) PUNCT bjmsr-311 55 17 . . PUNCT bjmsr-311 56 1 the the DET bjmsr-311 56 2 l1 l1 PROPN bjmsr-311 56 3 norm norm NOUN bjmsr-311 56 4 estimate estimate NOUN bjmsr-311 56 5 of of ADP bjmsr-311 56 6   PROPN bjmsr-311 56 7 is be AUX bjmsr-311 56 8 found find VERB bjmsr-311 56 9 by by ADP bjmsr-311 56 10 substituting substitute VERB bjmsr-311 56 11 the the DET bjmsr-311 56 12 values value NOUN bjmsr-311 56 13 of of ADP bjmsr-311 56 14 xt+1 xt+1 PROPN bjmsr-311 56 15 and and CCONJ bjmsr-311 56 16 yt+1 yt+1 NUM bjmsr-311 56 17 into into ADP bjmsr-311 56 18 ( ( PUNCT bjmsr-311 56 19 10 10 NUM bjmsr-311 56 20 ) ) PUNCT bjmsr-311 56 21 , , PUNCT bjmsr-311 56 22 ( ( PUNCT bjmsr-311 56 23 see see VERB bjmsr-311 56 24 , , PUNCT bjmsr-311 56 25 bidabad bidabad NOUN bjmsr-311 56 26 ( ( PUNCT bjmsr-311 56 27 1987a,88a 1987a,88a NUM bjmsr-311 56 28 ) ) PUNCT bjmsr-311 56 29 ) ) PUNCT bjmsr-311 56 30 . . PUNCT bjmsr-311 57 1 the the DET bjmsr-311 57 2 presented present VERB bjmsr-311 57 3 procedure procedure NOUN bjmsr-311 57 4 is be AUX bjmsr-311 57 5 essentially essentially ADV bjmsr-311 57 6 the the DET bjmsr-311 57 7 weighted weighted ADJ bjmsr-311 57 8 median median ADJ bjmsr-311 57 9 procedure procedure NOUN bjmsr-311 57 10 of of ADP bjmsr-311 57 11 laplace laplace NOUN bjmsr-311 57 12 ( ( PUNCT bjmsr-311 57 13 1818 1818 NUM bjmsr-311 57 14 ) ) PUNCT bjmsr-311 57 15 . . PUNCT bjmsr-311 58 1 namely namely ADV bjmsr-311 58 2 , , PUNCT bjmsr-311 58 3 this this DET bjmsr-311 58 4 solution solution NOUN bjmsr-311 58 5 is be AUX bjmsr-311 58 6 the the DET bjmsr-311 58 7 steps step NOUN bjmsr-311 58 8 that that PRON bjmsr-311 58 9 laplace laplace NOUN bjmsr-311 58 10 took take VERB bjmsr-311 58 11 . . PUNCT bjmsr-311 59 1 the the DET bjmsr-311 59 2 main main ADJ bjmsr-311 59 3 difference difference NOUN bjmsr-311 59 4 is be AUX bjmsr-311 59 5 the the DET bjmsr-311 59 6 mathematical mathematical ADJ bjmsr-311 59 7 derivation derivation NOUN bjmsr-311 59 8 . . PUNCT bjmsr-311 60 1 laplace laplace PROPN bjmsr-311 60 2 found find VERB bjmsr-311 60 3 this this DET bjmsr-311 60 4 solution solution NOUN bjmsr-311 60 5 by by ADP bjmsr-311 60 6 analyzing analyze VERB bjmsr-311 60 7 the the DET bjmsr-311 60 8 algebraic algebraic ADJ bjmsr-311 60 9 characteristic characteristic NOUN bjmsr-311 60 10 of of ADP bjmsr-311 60 11 the the DET bjmsr-311 60 12 l1 l1 PROPN bjmsr-311 60 13 norm norm PROPN bjmsr-311 60 14 objective objective ADJ bjmsr-311 60 15 function function NOUN bjmsr-311 60 16 ; ; PUNCT bjmsr-311 60 17 while while SCONJ bjmsr-311 60 18 the the DET bjmsr-311 60 19 above above ADJ bjmsr-311 60 20 procedure procedure NOUN bjmsr-311 60 21 exactly exactly ADV bjmsr-311 60 22 differentiates differentiate VERB bjmsr-311 60 23 the the DET bjmsr-311 60 24 objective objective ADJ bjmsr-311 60 25 function function NOUN bjmsr-311 60 26 . . PUNCT bjmsr-311 61 1 another another DET bjmsr-311 61 2 new new ADJ bjmsr-311 61 3 contribution contribution NOUN bjmsr-311 61 4 of of ADP bjmsr-311 61 5 this this DET bjmsr-311 61 6 procedure procedure NOUN bjmsr-311 61 7 is be AUX bjmsr-311 61 8 the the DET bjmsr-311 61 9 application application NOUN bjmsr-311 61 10 of of ADP bjmsr-311 61 11 the the DET bjmsr-311 61 12 partial partial ADJ bjmsr-311 61 13 discrete discrete ADJ bjmsr-311 61 14 differentiation differentiation NOUN bjmsr-311 61 15 over over ADP bjmsr-311 61 16 subscript subscript NOUN bjmsr-311 61 17 accompanying accompany VERB bjmsr-311 61 18 with with ADP bjmsr-311 61 19 conventional conventional ADJ bjmsr-311 61 20 differentiation differentiation NOUN bjmsr-311 61 21 on on ADP bjmsr-311 61 22 a a DET bjmsr-311 61 23 regular regular ADJ bjmsr-311 61 24 variable variable NOUN bjmsr-311 61 25 with with ADP bjmsr-311 61 26 the the DET bjmsr-311 61 27 continuous continuous ADJ bjmsr-311 61 28 domain domain NOUN bjmsr-311 61 29 . . PUNCT bjmsr-311 62 1 it it PRON bjmsr-311 62 2 should should AUX bjmsr-311 62 3 be be AUX bjmsr-311 62 4 remembered remember VERB bjmsr-311 62 5 that that SCONJ bjmsr-311 62 6 boscovich boscovich PROPN bjmsr-311 62 7 ( ( PUNCT bjmsr-311 62 8 1757 1757 NUM bjmsr-311 62 9 ) ) PUNCT bjmsr-311 62 10 solved solve VERB bjmsr-311 62 11 this this DET bjmsr-311 62 12 problem problem NOUN bjmsr-311 62 13 by by ADP bjmsr-311 62 14 a a DET bjmsr-311 62 15 geometrical geometrical ADJ bjmsr-311 62 16 procedure procedure NOUN bjmsr-311 62 17 and and CCONJ bjmsr-311 62 18 karst karst NOUN bjmsr-311 62 19 ( ( PUNCT bjmsr-311 62 20 1958 1958 NUM bjmsr-311 62 21 ) ) PUNCT bjmsr-311 62 22 by by ADP bjmsr-311 62 23 an an DET bjmsr-311 62 24 analytical analytical ADJ bjmsr-311 62 25 method method NOUN bjmsr-311 62 26 . . PUNCT bjmsr-311 63 1 2.1 2.1 NUM bjmsr-311 63 2 computation computation NOUN bjmsr-311 63 3 of of ADP bjmsr-311 63 4 weighted weight VERB bjmsr-311 63 5 median median PROPN bjmsr-311 63 6 two two NUM bjmsr-311 63 7 series series NOUN bjmsr-311 63 8 of of ADP bjmsr-311 63 9 computations computation NOUN bjmsr-311 63 10 are be AUX bjmsr-311 63 11 necessary necessary ADJ bjmsr-311 63 12 to to PART bjmsr-311 63 13 compute compute VERB bjmsr-311 63 14 the the DET bjmsr-311 63 15 weighted weighted ADJ bjmsr-311 63 16 median median NOUN bjmsr-311 63 17 . . PUNCT bjmsr-311 64 1 one one NUM bjmsr-311 64 2 sorting sort VERB bjmsr-311 64 3 algorithm algorithm NOUN bjmsr-311 64 4 is be AUX bjmsr-311 64 5 essential essential ADJ bjmsr-311 64 6 to to PART bjmsr-311 64 7 sort sort VERB bjmsr-311 64 8 the the DET bjmsr-311 64 9 z z NOUN bjmsr-311 64 10 array array NOUN bjmsr-311 64 11 and and CCONJ bjmsr-311 64 12 restoring restore VERB bjmsr-311 64 13 the the DET bjmsr-311 64 14 corresponding correspond VERB bjmsr-311 64 15 subscripts subscript NOUN bjmsr-311 64 16 to to PART bjmsr-311 64 17 compute compute VERB bjmsr-311 64 18 the the DET bjmsr-311 64 19 second second ADJ bjmsr-311 64 20 part part NOUN bjmsr-311 64 21 of of ADP bjmsr-311 64 22 the the DET bjmsr-311 64 23 calculation calculation NOUN bjmsr-311 64 24 to to PART bjmsr-311 64 25 find find VERB bjmsr-311 64 26 the the DET bjmsr-311 64 27 optimal optimal ADJ bjmsr-311 64 28 value value NOUN bjmsr-311 64 29 of of ADP bjmsr-311 64 30 k k PROPN bjmsr-311 64 31 by by ADP bjmsr-311 64 32 using use VERB bjmsr-311 64 33 dk dk PROPN bjmsr-311 64 34 defined define VERB bjmsr-311 64 35 by by ADP bjmsr-311 64 36 ( ( PUNCT bjmsr-311 64 37 11 11 NUM bjmsr-311 64 38 ) ) PUNCT bjmsr-311 64 39 . . PUNCT bjmsr-311 65 1 efficient efficient ADJ bjmsr-311 65 2 sorting sort VERB bjmsr-311 65 3 algorithms algorithm NOUN bjmsr-311 65 4 exist exist VERB bjmsr-311 65 5 for for ADP bjmsr-311 65 6 the the DET bjmsr-311 65 7 first first ADJ bjmsr-311 65 8 part part NOUN bjmsr-311 65 9 of of ADP bjmsr-311 65 10 the the DET bjmsr-311 65 11 computation computation NOUN bjmsr-311 65 12 . . PUNCT bjmsr-311 66 1 the the DET bjmsr-311 66 2 algorithms algorithm NOUN bjmsr-311 66 3 ' ' PUNCT bjmsr-311 66 4 quicksort quicksort NOUN bjmsr-311 66 5 ' ' PUNCT bjmsr-311 66 6 of of ADP bjmsr-311 66 7 hoare hoare PROPN bjmsr-311 66 8 ( ( PUNCT bjmsr-311 66 9 1961,62 1961,62 PROPN bjmsr-311 66 10 ) ) PUNCT bjmsr-311 66 11 , , PUNCT bjmsr-311 66 12 ' ' PUNCT bjmsr-311 66 13 quickersort quickersort NOUN bjmsr-311 66 14 ' ' PUNCT bjmsr-311 66 15 of of ADP bjmsr-311 66 16 scowen scowen NOUN bjmsr-311 66 17 ( ( PUNCT bjmsr-311 66 18 1965 1965 NUM bjmsr-311 66 19 ) ) PUNCT bjmsr-311 66 20 and and CCONJ bjmsr-311 66 21 ' ' PUNCT bjmsr-311 66 22 sort sort VERB bjmsr-311 66 23 ' ' PUNCT bjmsr-311 66 24 of of ADP bjmsr-311 66 25 singleton singleton PROPN bjmsr-311 66 26 ( ( PUNCT bjmsr-311 66 27 1969 1969 NUM bjmsr-311 66 28 ) ) PUNCT bjmsr-311 66 29 have have VERB bjmsr-311 66 30 desirable desirable ADJ bjmsr-311 66 31 performances performance NOUN bjmsr-311 66 32 and and CCONJ bjmsr-311 66 33 efficiencies efficiency NOUN bjmsr-311 66 34 . . PUNCT bjmsr-311 67 1 for for ADP bjmsr-311 67 2 the the DET bjmsr-311 67 3 second second ADJ bjmsr-311 67 4 part part NOUN bjmsr-311 67 5 of of ADP bjmsr-311 67 6 the the DET bjmsr-311 67 7 computation computation NOUN bjmsr-311 67 8 , , PUNCT bjmsr-311 67 9 there there PRON bjmsr-311 67 10 is be VERB bjmsr-311 67 11 no no DET bjmsr-311 67 12 special special ADJ bjmsr-311 67 13 purpose purpose NOUN bjmsr-311 67 14 procedure procedure NOUN bjmsr-311 67 15 , , PUNCT bjmsr-311 67 16 but but CCONJ bjmsr-311 67 17 bloomfield bloomfield PROPN bjmsr-311 67 18 and and CCONJ bjmsr-311 67 19 steiger steiger PROPN bjmsr-311 67 20 ( ( PUNCT bjmsr-311 67 21 1980 1980 NUM bjmsr-311 67 22 ) ) PUNCT bjmsr-311 67 23 used use VERB bjmsr-311 67 24 the the DET bjmsr-311 67 25 partial partial ADJ bjmsr-311 67 26 sorting sorting NOUN bjmsr-311 67 27 of of ADP bjmsr-311 67 28 chambers chamber NOUN bjmsr-311 67 29 ( ( PUNCT bjmsr-311 67 30 1971 1971 NUM bjmsr-311 67 31 ) ) PUNCT bjmsr-311 67 32 to to PART bjmsr-311 67 33 give give VERB bjmsr-311 67 34 an an DET bjmsr-311 67 35 efficient efficient ADJ bjmsr-311 67 36 way way NOUN bjmsr-311 67 37 to to PART bjmsr-311 67 38 combine combine VERB bjmsr-311 67 39 the the DET bjmsr-311 67 40 two two NUM bjmsr-311 67 41 steps step NOUN bjmsr-311 67 42 of of ADP bjmsr-311 67 43 sorting sort VERB bjmsr-311 67 44 the the DET bjmsr-311 67 45 z z NOUN bjmsr-311 67 46 array array NOUN bjmsr-311 67 47 and and CCONJ bjmsr-311 67 48 finding find VERB bjmsr-311 67 49 the the DET bjmsr-311 67 50 value value NOUN bjmsr-311 67 51 of of ADP bjmsr-311 67 52 k. k. PROPN bjmsr-311 67 53 the the DET bjmsr-311 67 54 superiority superiority NOUN bjmsr-311 67 55 of of ADP bjmsr-311 67 56 this this DET bjmsr-311 67 57 procedure procedure NOUN bjmsr-311 67 58 is be AUX bjmsr-311 67 59 in in ADP bjmsr-311 67 60 sorting sort VERB bjmsr-311 67 61 the the DET bjmsr-311 67 62 smaller small ADJ bjmsr-311 67 63 segments segment NOUN bjmsr-311 67 64 of of ADP bjmsr-311 67 65 z z PROPN bjmsr-311 67 66 array array NOUN bjmsr-311 67 67 rather rather ADV bjmsr-311 67 68 than than ADP bjmsr-311 67 69 all all DET bjmsr-311 67 70 its its PRON bjmsr-311 67 71 elements element NOUN bjmsr-311 67 72 . . PUNCT bjmsr-311 68 1 with with ADP bjmsr-311 68 2 some some DET bjmsr-311 68 3 modification modification NOUN bjmsr-311 68 4 , , PUNCT bjmsr-311 68 5 this this DET bjmsr-311 68 6 procedure procedure NOUN bjmsr-311 68 7 is be AUX bjmsr-311 68 8 used use VERB bjmsr-311 68 9 for for ADP bjmsr-311 68 10 our our PRON bjmsr-311 68 11 proposed propose VERB bjmsr-311 68 12 algorithms algorithm NOUN bjmsr-311 68 13 in in ADP bjmsr-311 68 14 the the DET bjmsr-311 68 15 forthcoming forthcoming ADJ bjmsr-311 68 16 sections section NOUN bjmsr-311 68 17 . . PUNCT bjmsr-311 69 1 this this DET bjmsr-311 69 2 procedure procedure NOUN bjmsr-311 69 3 can can AUX bjmsr-311 69 4 be be AUX bjmsr-311 69 5 stated state VERB bjmsr-311 69 6 as as ADP bjmsr-311 69 7 the the DET bjmsr-311 69 8 following follow VERB bjmsr-311 69 9 function function NOUN bjmsr-311 69 10 . . PUNCT bjmsr-311 70 1 function function NOUN bjmsr-311 70 2 lwmed lwme VERB bjmsr-311 70 3 ( ( PUNCT bjmsr-311 70 4 n n CCONJ bjmsr-311 70 5 , , PUNCT bjmsr-311 70 6 ys ys INTJ bjmsr-311 70 7 , , PUNCT bjmsr-311 70 8 w w NOUN bjmsr-311 70 9 , , PUNCT bjmsr-311 70 10 l l NOUN bjmsr-311 70 11 ) ) PUNCT bjmsr-311 70 12 step step NOUN bjmsr-311 70 13 0 0 NUM bjmsr-311 70 14 ) ) PUNCT bjmsr-311 70 15 initialization initialization NOUN bjmsr-311 70 16 . . PUNCT bjmsr-311 71 1 real real ADJ bjmsr-311 71 2 : : PUNCT bjmsr-311 71 3 ys(n ys(n NUM bjmsr-311 71 4 ) ) PUNCT bjmsr-311 71 5 , , PUNCT bjmsr-311 71 6 w(n w(n PROPN bjmsr-311 71 7 ) ) PUNCT bjmsr-311 71 8 . . PUNCT bjmsr-311 72 1 integer integer NOUN bjmsr-311 72 2 : : PUNCT bjmsr-311 72 3 l(n l(n PROPN bjmsr-311 72 4 ) ) PUNCT bjmsr-311 72 5 , , PUNCT bjmsr-311 72 6 hi hi INTJ bjmsr-311 72 7 . . PUNCT bjmsr-311 72 8 set set NOUN bjmsr-311 72 9 : : PUNCT bjmsr-311 72 10 ii=0 ii=0 NOUN bjmsr-311 72 11 , , PUNCT bjmsr-311 72 12 shi=0 shi=0 NOUN bjmsr-311 72 13 , , PUNCT bjmsr-311 72 14 slo=0 slo=0 NOUN bjmsr-311 72 15 , , PUNCT bjmsr-311 72 16 sz=0 sz=0 NOUN bjmsr-311 72 17 , , PUNCT bjmsr-311 72 18 sp=0 sp=0 NOUN bjmsr-311 72 19 , , PUNCT bjmsr-311 72 20 sn=0 sn=0 VERB bjmsr-311 72 21 . . PUNCT bjmsr-311 73 1 step step NOUN bjmsr-311 73 2 1 1 NUM bjmsr-311 73 3 ) ) PUNCT bjmsr-311 73 4 compute compute NOUN bjmsr-311 73 5 left leave VERB bjmsr-311 73 6 , , PUNCT bjmsr-311 73 7 middle middle ADJ bjmsr-311 73 8 and and CCONJ bjmsr-311 73 9 right right ADJ bjmsr-311 73 10 sum sum NOUN bjmsr-311 73 11 of of ADP bjmsr-311 73 12 weights weight NOUN bjmsr-311 73 13 . . PUNCT bjmsr-311 74 1 do do AUX bjmsr-311 74 2 loop loop VERB bjmsr-311 74 3 for for ADP bjmsr-311 74 4 i=1,n i=1,n NOUN bjmsr-311 74 5 : : PUNCT bjmsr-311 74 6 w(i)=|w(i)| w(i)=|w(i)| NUM bjmsr-311 74 7 ; ; PUNCT bjmsr-311 74 8 if if SCONJ bjmsr-311 74 9 ys(i)<0 ys(i)<0 NUM bjmsr-311 74 10 , , PUNCT bjmsr-311 74 11 then then ADV bjmsr-311 74 12 sn sn NOUN bjmsr-311 74 13 = = NOUN bjmsr-311 74 14 sn+w(i sn+w(i NOUN bjmsr-311 74 15 ) ) PUNCT bjmsr-311 74 16 , , PUNCT bjmsr-311 74 17 if if SCONJ bjmsr-311 74 18 ys(i)>0 ys(i)>0 PROPN bjmsr-311 74 19 , , PUNCT bjmsr-311 74 20 then then ADV bjmsr-311 74 21 sp sp VERB bjmsr-311 74 22 = = NOUN bjmsr-311 74 23 sp+w(i sp+w(i X bjmsr-311 74 24 ) ) PUNCT bjmsr-311 74 25 , , PUNCT bjmsr-311 74 26 if if SCONJ bjmsr-311 74 27 ys(i)=0 ys(i)=0 PROPN bjmsr-311 74 28 then then ADV bjmsr-311 74 29 sz sz NOUN bjmsr-311 74 30 = = NOUN bjmsr-311 74 31 sz+w(i sz+w(i NOUN bjmsr-311 74 32 ) ) PUNCT bjmsr-311 74 33 ; ; PUNCT bjmsr-311 74 34 end end NOUN bjmsr-311 74 35 do do VERB bjmsr-311 74 36 . . PUNCT bjmsr-311 75 1 if if SCONJ bjmsr-311 75 2 shi≤slo shi≤slo PROPN bjmsr-311 75 3 then then ADV bjmsr-311 75 4 go go VERB bjmsr-311 75 5 to to PART bjmsr-311 75 6 step step VERB bjmsr-311 75 7 2.b 2.b NUM bjmsr-311 75 8 , , PUNCT bjmsr-311 75 9 otherwise otherwise ADV bjmsr-311 75 10 go go VERB bjmsr-311 75 11 to to PART bjmsr-311 75 12 step step VERB bjmsr-311 75 13 2.a 2.a NUM bjmsr-311 75 14 . . PUNCT bjmsr-311 76 1 step step NOUN bjmsr-311 76 2 2 2 NUM bjmsr-311 76 3 ) ) PUNCT bjmsr-311 76 4 assign assign VERB bjmsr-311 76 5 subscripts subscript NOUN bjmsr-311 76 6 for for ADP bjmsr-311 76 7 arrays array NOUN bjmsr-311 76 8 . . PUNCT bjmsr-311 77 1 copyright copyright NOUN bjmsr-311 77 2 © © PROPN bjmsr-311 77 3 cc cc PROPN bjmsr-311 77 4 - - PUNCT bjmsr-311 77 5 by by ADP bjmsr-311 77 6 - - PUNCT bjmsr-311 77 7 nc nc PROPN bjmsr-311 77 8 2019 2019 NUM bjmsr-311 77 9 , , PUNCT bjmsr-311 77 10 bjmsr bjmsr PROPN bjmsr-311 77 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 78 1 bangladesh bangladesh PROPN bjmsr-311 78 2 journal journal PROPN bjmsr-311 78 3 of of ADP bjmsr-311 78 4 multidisciplinary multidisciplinary ADJ bjmsr-311 78 5 scientific scientific ADJ bjmsr-311 78 6 research research NOUN bjmsr-311 78 7 vol vol NOUN bjmsr-311 78 8 . . PROPN bjmsr-311 78 9 1 1 NUM bjmsr-311 78 10 , , PUNCT bjmsr-311 78 11 no no INTJ bjmsr-311 78 12 . . NOUN bjmsr-311 78 13 1 1 NUM bjmsr-311 78 14 ; ; PUNCT bjmsr-311 78 15 2019 2019 NUM bjmsr-311 78 16 4 4 NUM bjmsr-311 78 17 a. a. NOUN bjmsr-311 78 18 let let NOUN bjmsr-311 78 19 : : PUNCT bjmsr-311 78 20 shi=0 shi=0 VERB bjmsr-311 78 21 . . PUNCT bjmsr-311 79 1 do do AUX bjmsr-311 79 2 loop loop VERB bjmsr-311 79 3 for for ADP bjmsr-311 79 4 i=1,n i=1,n NOUN bjmsr-311 79 5 : : PUNCT bjmsr-311 79 6 if if SCONJ bjmsr-311 79 7 ys(i ys(i NUM bjmsr-311 79 8 ) ) PUNCT bjmsr-311 80 1 ≤0 ≤0 NOUN bjmsr-311 80 2 go go VERB bjmsr-311 80 3 to to PART bjmsr-311 80 4 continue continue VERB bjmsr-311 80 5 , , PUNCT bjmsr-311 80 6 otherwise otherwise ADV bjmsr-311 80 7 ii ii VERB bjmsr-311 80 8 = = NOUN bjmsr-311 80 9 ii+1 ii+1 NOUN bjmsr-311 80 10 , , PUNCT bjmsr-311 80 11 l(ii)=i l(ii)=i ADJ bjmsr-311 80 12 , , PUNCT bjmsr-311 80 13 continue continue VERB bjmsr-311 80 14 , , PUNCT bjmsr-311 80 15 end end VERB bjmsr-311 80 16 do do VERB bjmsr-311 80 17 . . PUNCT bjmsr-311 81 1 go go VERB bjmsr-311 81 2 to to PART bjmsr-311 81 3 step step VERB bjmsr-311 81 4 2.c 2.c NUM bjmsr-311 81 5 . . PUNCT bjmsr-311 82 1 b. b. PROPN bjmsr-311 83 1 let let VERB bjmsr-311 83 2 : : PUNCT bjmsr-311 83 3 slo=0 slo=0 VERB bjmsr-311 83 4 . . PUNCT bjmsr-311 84 1 do do AUX bjmsr-311 84 2 loop loop VERB bjmsr-311 84 3 for for ADP bjmsr-311 84 4 i=1,n i=1,n NOUN bjmsr-311 84 5 : : PUNCT bjmsr-311 84 6 if if SCONJ bjmsr-311 84 7 ys(i)>0 ys(i)>0 PROPN bjmsr-311 84 8 go go VERB bjmsr-311 84 9 to to PART bjmsr-311 84 10 continue continue VERB bjmsr-311 84 11 , , PUNCT bjmsr-311 84 12 otherwise otherwise ADV bjmsr-311 84 13 ii ii VERB bjmsr-311 84 14 = = NOUN bjmsr-311 84 15 ii+1 ii+1 NOUN bjmsr-311 84 16 , , PUNCT bjmsr-311 84 17 l(ii)=i l(ii)=i ADJ bjmsr-311 84 18 , , PUNCT bjmsr-311 84 19 continue continue VERB bjmsr-311 84 20 , , PUNCT bjmsr-311 84 21 end end VERB bjmsr-311 84 22 do do AUX bjmsr-311 84 23 . . PUNCT bjmsr-311 85 1 c. c. PROPN bjmsr-311 85 2 let let VERB bjmsr-311 85 3 : : PUNCT bjmsr-311 85 4 lo=1 lo=1 PROPN bjmsr-311 85 5 , , PUNCT bjmsr-311 85 6 hi hi PROPN bjmsr-311 85 7 = = PROPN bjmsr-311 85 8 ii ii NOUN bjmsr-311 85 9 . . PUNCT bjmsr-311 86 1 step step NOUN bjmsr-311 86 2 3 3 NUM bjmsr-311 86 3 ) ) PUNCT bjmsr-311 86 4 check check NOUN bjmsr-311 86 5 for for ADP bjmsr-311 86 6 solution solution NOUN bjmsr-311 86 7 . . PUNCT bjmsr-311 87 1 if if SCONJ bjmsr-311 87 2 hi hi INTJ bjmsr-311 87 3 > > X bjmsr-311 87 4 lo+1 lo+1 NUM bjmsr-311 87 5 then then ADV bjmsr-311 87 6 go go VERB bjmsr-311 87 7 to to PART bjmsr-311 87 8 step step VERB bjmsr-311 87 9 4 4 NUM bjmsr-311 87 10 , , PUNCT bjmsr-311 87 11 otherwise otherwise ADV bjmsr-311 87 12 lwmed lwme VERB bjmsr-311 87 13 = = PRON bjmsr-311 87 14 l(lo l(lo NUM bjmsr-311 87 15 ) ) PUNCT bjmsr-311 87 16 . . PUNCT bjmsr-311 88 1 if if SCONJ bjmsr-311 88 2 lo lo PROPN bjmsr-311 88 3 = = NOUN bjmsr-311 88 4 hi hi NOUN bjmsr-311 88 5 return return NOUN bjmsr-311 88 6 , , PUNCT bjmsr-311 88 7 otherwise otherwise ADV bjmsr-311 88 8 if if SCONJ bjmsr-311 88 9 ys(l(lo ys(l(lo NUM bjmsr-311 88 10 ) ) PUNCT bjmsr-311 88 11 ) ) PUNCT bjmsr-311 88 12 ≤ys(l(hi ≤ys(l(hi PROPN bjmsr-311 88 13 ) ) PUNCT bjmsr-311 88 14 ) ) PUNCT bjmsr-311 88 15 go go VERB bjmsr-311 88 16 to to PART bjmsr-311 88 17 step step VERB bjmsr-311 88 18 3.a 3.a NUM bjmsr-311 88 19 , , PUNCT bjmsr-311 88 20 otherwise otherwise ADV bjmsr-311 88 21 lt lt PROPN bjmsr-311 88 22 = = PROPN bjmsr-311 88 23 l(lo l(lo PROPN bjmsr-311 88 24 ) ) PUNCT bjmsr-311 88 25 , , PUNCT bjmsr-311 88 26 l(lo)=l(hi l(lo)=l(hi NOUN bjmsr-311 88 27 ) ) PUNCT bjmsr-311 88 28 , , PUNCT bjmsr-311 88 29 l(hi)=lt l(hi)=lt PROPN bjmsr-311 88 30 , , PUNCT bjmsr-311 88 31 lwmed lwme VERB bjmsr-311 88 32 = = PRON bjmsr-311 88 33 l(lo l(lo NUM bjmsr-311 88 34 ) ) PUNCT bjmsr-311 88 35 . . PUNCT bjmsr-311 89 1 a. a. NOUN bjmsr-311 90 1 if if SCONJ bjmsr-311 90 2 shi+w(l(hi))>slo+w(l(lo shi+w(l(hi))>slo+w(l(lo VERB bjmsr-311 90 3 ) ) PUNCT bjmsr-311 90 4 ) ) PUNCT bjmsr-311 91 1 then then ADV bjmsr-311 91 2 set set VERB bjmsr-311 91 3 lwmed lwmed ADJ bjmsr-311 91 4 = = SYM bjmsr-311 91 5 l(hi l(hi PROPN bjmsr-311 91 6 ) ) PUNCT bjmsr-311 91 7 , , PUNCT bjmsr-311 91 8 otherwise otherwise ADV bjmsr-311 91 9 return return VERB bjmsr-311 91 10 . . PUNCT bjmsr-311 92 1 step step NOUN bjmsr-311 92 2 4 4 NUM bjmsr-311 92 3 ) ) PUNCT bjmsr-311 92 4 divide divide VERB bjmsr-311 92 5 the the DET bjmsr-311 92 6 string string NOUN bjmsr-311 92 7 into into ADP bjmsr-311 92 8 two two NUM bjmsr-311 92 9 halves half NOUN bjmsr-311 92 10 then then ADV bjmsr-311 92 11 sort sort ADV bjmsr-311 92 12 . . PUNCT bjmsr-311 93 1 set set NOUN bjmsr-311 93 2 : : PUNCT bjmsr-311 93 3 mid=(lo+hi)/2 mid=(lo+hi)/2 PROPN bjmsr-311 93 4 , , PUNCT bjmsr-311 93 5 lop lop NOUN bjmsr-311 93 6 = = SYM bjmsr-311 93 7 lo+1 lo+1 PROPN bjmsr-311 93 8 , , PUNCT bjmsr-311 93 9 lt lt PROPN bjmsr-311 93 10 = = PROPN bjmsr-311 93 11 l(mid l(mid PROPN bjmsr-311 93 12 ) ) PUNCT bjmsr-311 93 13 , , PUNCT bjmsr-311 93 14 l(mid)=l(lop l(mid)=l(lop NOUN bjmsr-311 93 15 ) ) PUNCT bjmsr-311 93 16 , , PUNCT bjmsr-311 93 17 l(lop)=lt l(lop)=lt PROPN bjmsr-311 93 18 . . PUNCT bjmsr-311 93 19 a. a. NOUN bjmsr-311 94 1 if if SCONJ bjmsr-311 94 2 ys(l(lop ys(l(lop PROPN bjmsr-311 94 3 ) ) PUNCT bjmsr-311 94 4 ) ) PUNCT bjmsr-311 95 1 ≤ys(l(hi ≤ys(l(hi PROPN bjmsr-311 95 2 ) ) PUNCT bjmsr-311 95 3 ) ) PUNCT bjmsr-311 95 4 then then ADV bjmsr-311 95 5 go go VERB bjmsr-311 95 6 to to PART bjmsr-311 95 7 step step VERB bjmsr-311 95 8 4.b 4.b NUM bjmsr-311 95 9 , , PUNCT bjmsr-311 95 10 otherwise otherwise ADV bjmsr-311 95 11 lt lt PROPN bjmsr-311 95 12 = = NOUN bjmsr-311 95 13 l(lop l(lop NOUN bjmsr-311 95 14 ) ) PUNCT bjmsr-311 95 15 , , PUNCT bjmsr-311 95 16 l(lop)=l(hi l(lop)=l(hi PROPN bjmsr-311 95 17 ) ) PUNCT bjmsr-311 95 18 , , PUNCT bjmsr-311 95 19 l(hi)=lt l(hi)=lt PROPN bjmsr-311 95 20 . . PUNCT bjmsr-311 95 21 b. b. PROPN bjmsr-311 96 1 if if SCONJ bjmsr-311 96 2 ys(l(lo ys(l(lo PROPN bjmsr-311 96 3 ) ) PUNCT bjmsr-311 96 4 ) ) PUNCT bjmsr-311 97 1 ≤ys(l(hi ≤ys(l(hi PROPN bjmsr-311 97 2 ) ) PUNCT bjmsr-311 97 3 ) ) PUNCT bjmsr-311 97 4 then then ADV bjmsr-311 97 5 go go VERB bjmsr-311 97 6 to to PART bjmsr-311 97 7 step step NOUN bjmsr-311 97 8 4.c 4.c NUM bjmsr-311 97 9 , , PUNCT bjmsr-311 97 10 otherwise otherwise ADV bjmsr-311 97 11 lt lt PROPN bjmsr-311 97 12 = = PROPN bjmsr-311 97 13 l(lo l(lo PROPN bjmsr-311 97 14 ) ) PUNCT bjmsr-311 97 15 , , PUNCT bjmsr-311 97 16 l(lo)=l(hi l(lo)=l(hi NOUN bjmsr-311 97 17 ) ) PUNCT bjmsr-311 97 18 , , PUNCT bjmsr-311 97 19 l(hi)=lt l(hi)=lt PROPN bjmsr-311 97 20 . . PUNCT bjmsr-311 97 21 c. c. PROPN bjmsr-311 98 1 if if SCONJ bjmsr-311 98 2 ys(l(lop ys(l(lop PROPN bjmsr-311 98 3 ) ) PUNCT bjmsr-311 98 4 ) ) PUNCT bjmsr-311 99 1 ≤ys(l(lo ≤ys(l(lo PROPN bjmsr-311 99 2 ) ) PUNCT bjmsr-311 99 3 ) ) PUNCT bjmsr-311 99 4 then then ADV bjmsr-311 99 5 go go VERB bjmsr-311 99 6 to to PART bjmsr-311 99 7 step step VERB bjmsr-311 99 8 5 5 NUM bjmsr-311 99 9 , , PUNCT bjmsr-311 99 10 otherwise otherwise ADV bjmsr-311 99 11 lt lt PROPN bjmsr-311 99 12 = = NOUN bjmsr-311 99 13 l(lop l(lop NOUN bjmsr-311 99 14 ) ) PUNCT bjmsr-311 99 15 , , PUNCT bjmsr-311 99 16 l(lop)=l(lo l(lop)=l(lo PROPN bjmsr-311 99 17 ) ) PUNCT bjmsr-311 99 18 , , PUNCT bjmsr-311 99 19 l(lo)=lt l(lo)=lt PROPN bjmsr-311 99 20 . . PUNCT bjmsr-311 99 21 step step NOUN bjmsr-311 99 22 5 5 NUM bjmsr-311 99 23 ) ) PUNCT bjmsr-311 99 24 compute compute VERB bjmsr-311 99 25 the the DET bjmsr-311 99 26 accumulation accumulation NOUN bjmsr-311 99 27 of of ADP bjmsr-311 99 28 weights weight NOUN bjmsr-311 99 29 . . PUNCT bjmsr-311 100 1 let let VERB bjmsr-311 100 2 : : PUNCT bjmsr-311 100 3 lwmed lwmed VERB bjmsr-311 100 4 = = SYM bjmsr-311 100 5 l(lo l(lo NUM bjmsr-311 100 6 ) ) PUNCT bjmsr-311 100 7 , , PUNCT bjmsr-311 100 8 i i PROPN bjmsr-311 100 9 = = NOUN bjmsr-311 100 10 lop lop PROPN bjmsr-311 100 11 , , PUNCT bjmsr-311 100 12 j j X bjmsr-311 100 13 = = X bjmsr-311 100 14 hi hi PROPN bjmsr-311 100 15 , , PUNCT bjmsr-311 100 16 xt xt X bjmsr-311 100 17 = = X bjmsr-311 100 18 ys(lwmed ys(lwme VERB bjmsr-311 100 19 ) ) PUNCT bjmsr-311 100 20 , , PUNCT bjmsr-311 100 21 tlo tlo PROPN bjmsr-311 100 22 = = SYM bjmsr-311 100 23 slo slo PROPN bjmsr-311 100 24 , , PUNCT bjmsr-311 100 25 thi thi PROPN bjmsr-311 100 26 = = PROPN bjmsr-311 100 27 shi shi PROPN bjmsr-311 100 28 . . PUNCT bjmsr-311 101 1 a. a. PROPN bjmsr-311 101 2 set set PROPN bjmsr-311 101 3 : : PUNCT bjmsr-311 101 4 tlo tlo PROPN bjmsr-311 101 5 = = PUNCT bjmsr-311 101 6 tlo+w(l(i tlo+w(l(i NOUN bjmsr-311 101 7 ) ) PUNCT bjmsr-311 101 8 ) ) PUNCT bjmsr-311 101 9 , , PUNCT bjmsr-311 101 10 i i PRON bjmsr-311 101 11 = = NOUN bjmsr-311 101 12 i+1 i+1 VERB bjmsr-311 101 13 . . PUNCT bjmsr-311 102 1 if if SCONJ bjmsr-311 102 2 ys(l(i))xt ys(l(j))>xt PROPN bjmsr-311 104 3 then then ADV bjmsr-311 104 4 go go VERB bjmsr-311 104 5 to to PART bjmsr-311 104 6 step step VERB bjmsr-311 104 7 5.b 5.b NUM bjmsr-311 104 8 , , PUNCT bjmsr-311 104 9 otherwise otherwise ADV bjmsr-311 104 10 if if SCONJ bjmsr-311 104 11 j≤i j≤i NOUN bjmsr-311 104 12 then then ADV bjmsr-311 104 13 go go VERB bjmsr-311 104 14 to to PART bjmsr-311 104 15 step step VERB bjmsr-311 104 16 6 6 NUM bjmsr-311 104 17 , , PUNCT bjmsr-311 104 18 otherwise otherwise ADV bjmsr-311 104 19 lt lt PROPN bjmsr-311 104 20 = = NOUN bjmsr-311 104 21 l(i l(i NOUN bjmsr-311 104 22 ) ) PUNCT bjmsr-311 104 23 , , PUNCT bjmsr-311 104 24 l(i)=l(j l(i)=l(j NOUN bjmsr-311 104 25 ) ) PUNCT bjmsr-311 104 26 , , PUNCT bjmsr-311 104 27 l(j)=lt l(j)=lt NOUN bjmsr-311 104 28 , , PUNCT bjmsr-311 104 29 go go VERB bjmsr-311 104 30 to to PART bjmsr-311 104 31 step step VERB bjmsr-311 104 32 5.a 5.a NUM bjmsr-311 104 33 . . PUNCT bjmsr-311 105 1 step step NOUN bjmsr-311 105 2 6 6 NUM bjmsr-311 105 3 ) ) PUNCT bjmsr-311 105 4 test test NOUN bjmsr-311 105 5 for for ADP bjmsr-311 105 6 solution solution NOUN bjmsr-311 105 7 . . PUNCT bjmsr-311 106 1 let let VERB bjmsr-311 106 2 : : PUNCT bjmsr-311 106 3 test test NOUN bjmsr-311 106 4 = = SYM bjmsr-311 106 5 w(lwmed w(lwme VERB bjmsr-311 106 6 ) ) PUNCT bjmsr-311 106 7 . . PUNCT bjmsr-311 107 1 if if SCONJ bjmsr-311 107 2 i≠j i≠j NOUN bjmsr-311 107 3 then then ADV bjmsr-311 107 4 go go VERB bjmsr-311 107 5 to to PART bjmsr-311 107 6 step step VERB bjmsr-311 107 7 6.a 6.a NUM bjmsr-311 107 8 , , PUNCT bjmsr-311 107 9 otherwise otherwise ADV bjmsr-311 107 10 test test NOUN bjmsr-311 107 11 = = SYM bjmsr-311 107 12 test+w(l(i test+w(l(i NOUN bjmsr-311 107 13 ) ) PUNCT bjmsr-311 107 14 ) ) PUNCT bjmsr-311 107 15 , , PUNCT bjmsr-311 107 16 i i PRON bjmsr-311 107 17 = = VERB bjmsr-311 107 18 i+1 i+1 PROPN bjmsr-311 107 19 , , PUNCT bjmsr-311 107 20 j j NOUN bjmsr-311 107 21 = = NOUN bjmsr-311 107 22 j-1 j-1 ADV bjmsr-311 107 23 . . PUNCT bjmsr-311 108 1 a. a. NOUN bjmsr-311 109 1 if if SCONJ bjmsr-311 109 2 test≥|thi test≥|thi NOUN bjmsr-311 109 3 - - PUNCT bjmsr-311 109 4 tlo| tlo| NOUN bjmsr-311 109 5 then then ADV bjmsr-311 109 6 return return VERB bjmsr-311 109 7 , , PUNCT bjmsr-311 109 8 otherwise otherwise ADV bjmsr-311 109 9 , , PUNCT bjmsr-311 109 10 if if SCONJ bjmsr-311 109 11 tlo tlo PROPN bjmsr-311 109 12 > > X bjmsr-311 109 13 thi thi AUX bjmsr-311 109 14 then then ADV bjmsr-311 109 15 step step VERB bjmsr-311 109 16 6.b 6.b NUM bjmsr-311 109 17 , , PUNCT bjmsr-311 109 18 otherwise otherwise ADV bjmsr-311 109 19 slo slo PROPN bjmsr-311 109 20 = = PROPN bjmsr-311 109 21 tlo+test tlo+test ADJ bjmsr-311 109 22 , , PUNCT bjmsr-311 109 23 lo lo PROPN bjmsr-311 109 24 = = PROPN bjmsr-311 109 25 i i PROPN bjmsr-311 109 26 , , PUNCT bjmsr-311 109 27 go go VERB bjmsr-311 109 28 to to PART bjmsr-311 109 29 step step VERB bjmsr-311 109 30 3 3 NUM bjmsr-311 109 31 . . PUNCT bjmsr-311 110 1 b. b. PROPN bjmsr-311 110 2 let let VERB bjmsr-311 110 3 : : PUNCT bjmsr-311 110 4 shi shi PROPN bjmsr-311 110 5 = = PROPN bjmsr-311 110 6 thi+test thi+t ADJ bjmsr-311 110 7 , , PUNCT bjmsr-311 110 8 lo lo PROPN bjmsr-311 110 9 = = NOUN bjmsr-311 110 10 lop lop NOUN bjmsr-311 110 11 , , PUNCT bjmsr-311 110 12 hi hi PROPN bjmsr-311 110 13 = = VERB bjmsr-311 110 14 j. j. PROPN bjmsr-311 110 15 go go VERB bjmsr-311 110 16 to to PART bjmsr-311 110 17 step step VERB bjmsr-311 110 18 3 3 NUM bjmsr-311 110 19 . . PUNCT bjmsr-311 110 20 end end VERB bjmsr-311 110 21 2.2 2.2 NUM bjmsr-311 110 22 discussion discussion NOUN bjmsr-311 110 23 of of ADP bjmsr-311 110 24 the the DET bjmsr-311 110 25 m m PROPN bjmsr-311 110 26 parameters parameter NOUN bjmsr-311 110 27 model model VERB bjmsr-311 110 28 the the DET bjmsr-311 110 29 procedure procedure NOUN bjmsr-311 110 30 applied apply VERB bjmsr-311 110 31 to to ADP bjmsr-311 110 32 the the DET bjmsr-311 110 33 simple simple ADJ bjmsr-311 110 34 one one NUM bjmsr-311 110 35 - - PUNCT bjmsr-311 110 36 parameter parameter NOUN bjmsr-311 110 37 model model NOUN bjmsr-311 110 38 can can AUX bjmsr-311 110 39 not not PART bjmsr-311 110 40 be be AUX bjmsr-311 110 41 simply simply ADV bjmsr-311 110 42 generalized generalize VERB bjmsr-311 110 43 to to ADP bjmsr-311 110 44 the the DET bjmsr-311 110 45 m m PROPN bjmsr-311 110 46 parameters parameter NOUN bjmsr-311 110 47 model model NOUN bjmsr-311 110 48 . . PUNCT bjmsr-311 111 1 this this DET bjmsr-311 111 2 difficulty difficulty NOUN bjmsr-311 111 3 is be AUX bjmsr-311 111 4 due due ADJ bjmsr-311 111 5 to to ADP bjmsr-311 111 6 the the DET bjmsr-311 111 7 fact fact NOUN bjmsr-311 111 8 that that SCONJ bjmsr-311 111 9 we we PRON bjmsr-311 111 10 can can AUX bjmsr-311 111 11 not not PART bjmsr-311 111 12 reorder reorder VERB bjmsr-311 111 13 observations observation NOUN bjmsr-311 111 14 in in ADP bjmsr-311 111 15 such such DET bjmsr-311 111 16 a a DET bjmsr-311 111 17 way way NOUN bjmsr-311 111 18 that that PRON bjmsr-311 111 19 their their PRON bjmsr-311 111 20 corresponding correspond VERB bjmsr-311 111 21 residuals residual NOUN bjmsr-311 111 22 are be AUX bjmsr-311 111 23 increasingly increasingly ADV bjmsr-311 111 24 or or CCONJ bjmsr-311 111 25 decreasingly decreasingly ADV bjmsr-311 111 26 ordered order VERB bjmsr-311 111 27 . . PUNCT bjmsr-311 112 1 on on ADP bjmsr-311 112 2 the the DET bjmsr-311 112 3 other other ADJ bjmsr-311 112 4 hand hand NOUN bjmsr-311 112 5 , , PUNCT bjmsr-311 112 6 to to PART bjmsr-311 112 7 apply apply VERB bjmsr-311 112 8 the the DET bjmsr-311 112 9 discrete discrete ADJ bjmsr-311 112 10 differentiation differentiation NOUN bjmsr-311 112 11 technique technique NOUN bjmsr-311 112 12 , , PUNCT bjmsr-311 112 13 primarily primarily ADV bjmsr-311 112 14 ( ( PUNCT bjmsr-311 112 15 2 2 X bjmsr-311 112 16 ) ) PUNCT bjmsr-311 112 17 should should AUX bjmsr-311 112 18 be be AUX bjmsr-311 112 19 rewritten rewrite VERB bjmsr-311 112 20 as as SCONJ bjmsr-311 112 21 follows follow VERB bjmsr-311 112 22 : : PUNCT bjmsr-311 112 23 t t PROPN bjmsr-311 112 24 m m VERB bjmsr-311 112 25 n n PRON bjmsr-311 112 26 m m PROPN bjmsr-311 112 27 s s NOUN bjmsr-311 112 28 = = X bjmsr-311 112 29   ADJ bjmsr-311 112 30 ( ( PUNCT bjmsr-311 112 31 yh yh PROPN bjmsr-311 112 32   VERB bjmsr-311 112 33 ßjxjh ßjxjh NOUN bjmsr-311 112 34 ) ) PUNCT bjmsr-311 112 35   PROPN bjmsr-311 112 36 ( ( PUNCT bjmsr-311 112 37 yh yh PROPN bjmsr-311 112 38   PROPN bjmsr-311 112 39 ßjxjh ßjxjh PROPN bjmsr-311 112 40 ) ) PUNCT bjmsr-311 112 41 ( ( PUNCT bjmsr-311 112 42 12 12 NUM bjmsr-311 112 43 ) ) PUNCT bjmsr-311 112 44 h=1 h=1 NOUN bjmsr-311 113 1 j=1 j=1 NOUN bjmsr-311 113 2 h h NOUN bjmsr-311 113 3 = = NOUN bjmsr-311 113 4 t+1 t+1 PROPN bjmsr-311 113 5 j=1 j=1 ADJ bjmsr-311 113 6 expression expression NOUN bjmsr-311 113 7 ( ( PUNCT bjmsr-311 113 8 12 12 NUM bjmsr-311 113 9 ) ) PUNCT bjmsr-311 113 10 , , PUNCT bjmsr-311 113 11 which which PRON bjmsr-311 113 12 is be AUX bjmsr-311 113 13 free free ADJ bjmsr-311 113 14 of of ADP bjmsr-311 113 15 absolute absolute ADJ bjmsr-311 113 16 value value NOUN bjmsr-311 113 17 sign sign NOUN bjmsr-311 113 18 is be AUX bjmsr-311 113 19 the the DET bjmsr-311 113 20 generalization generalization NOUN bjmsr-311 113 21 of of ADP bjmsr-311 113 22 ( ( PUNCT bjmsr-311 113 23 8) 8) NUM bjmsr-311 113 24 for for ADP bjmsr-311 113 25 m m NOUN bjmsr-311 113 26 parameters parameter NOUN bjmsr-311 113 27 . . PUNCT bjmsr-311 114 1 but but CCONJ bjmsr-311 114 2 our our PRON bjmsr-311 114 3 first first ADJ bjmsr-311 114 4 problem problem NOUN bjmsr-311 114 5 is be AUX bjmsr-311 114 6 to to PART bjmsr-311 114 7 find find VERB bjmsr-311 114 8 a a DET bjmsr-311 114 9 logic logic NOUN bjmsr-311 114 10 which which PRON bjmsr-311 114 11 enables enable VERB bjmsr-311 114 12 us we PRON bjmsr-311 114 13 to to PART bjmsr-311 114 14 form form VERB bjmsr-311 114 15 ( ( PUNCT bjmsr-311 114 16 12 12 NUM bjmsr-311 114 17 ) ) PUNCT bjmsr-311 114 18 . . PUNCT bjmsr-311 115 1 on on ADP bjmsr-311 115 2 the the DET bjmsr-311 115 3 other other ADJ bjmsr-311 115 4 hand hand NOUN bjmsr-311 115 5 , , PUNCT bjmsr-311 115 6 we we PRON bjmsr-311 115 7 need need VERB bjmsr-311 115 8 to to PART bjmsr-311 115 9 reorder reorder VERB bjmsr-311 115 10 observations observation NOUN bjmsr-311 115 11 in in ADP bjmsr-311 115 12 such such DET bjmsr-311 115 13 a a DET bjmsr-311 115 14 way way NOUN bjmsr-311 115 15 that that SCONJ bjmsr-311 115 16 when when SCONJ bjmsr-311 115 17 h h NOUN bjmsr-311 115 18 is be AUX bjmsr-311 115 19 less less ADJ bjmsr-311 115 20 , , PUNCT bjmsr-311 115 21 equal equal ADJ bjmsr-311 115 22 or or CCONJ bjmsr-311 115 23 greater great ADJ bjmsr-311 115 24 than than ADP bjmsr-311 115 25 t+1 t+1 PROPN bjmsr-311 115 26 , , PUNCT bjmsr-311 115 27 uh uh INTJ bjmsr-311 115 28 be be AUX bjmsr-311 115 29 greater great ADJ bjmsr-311 115 30 , , PUNCT bjmsr-311 115 31 equal equal ADJ bjmsr-311 115 32 or or CCONJ bjmsr-311 115 33 less less ADJ bjmsr-311 115 34 than than ADP bjmsr-311 115 35 zero zero NUM bjmsr-311 115 36 respectively respectively ADV bjmsr-311 115 37 ; ; PUNCT bjmsr-311 115 38 and and CCONJ bjmsr-311 115 39 as as SCONJ bjmsr-311 115 40 h h NOUN bjmsr-311 115 41 increases increase VERB bjmsr-311 115 42 from from ADP bjmsr-311 115 43 one one NUM bjmsr-311 115 44 to to ADP bjmsr-311 115 45 n n CCONJ bjmsr-311 115 46 , , PUNCT bjmsr-311 115 47 the the DET bjmsr-311 115 48 corresponding corresponding ADJ bjmsr-311 115 49 residual residual ADJ bjmsr-311 115 50 uh uh INTJ bjmsr-311 115 51 decreases decrease NOUN bjmsr-311 115 52 accordingly accordingly ADV bjmsr-311 115 53 . . PUNCT bjmsr-311 116 1 if if SCONJ bjmsr-311 116 2 ( ( PUNCT bjmsr-311 116 3 2 2 X bjmsr-311 116 4 ) ) PUNCT bjmsr-311 116 5 could could AUX bjmsr-311 116 6 be be AUX bjmsr-311 116 7 written write VERB bjmsr-311 116 8 as as ADP bjmsr-311 116 9 ( ( PUNCT bjmsr-311 116 10 12 12 NUM bjmsr-311 116 11 ) ) PUNCT bjmsr-311 116 12 , , PUNCT bjmsr-311 116 13 we we PRON bjmsr-311 116 14 could could AUX bjmsr-311 116 15 again again ADV bjmsr-311 116 16 differentiate differentiate VERB bjmsr-311 116 17 it it PRON bjmsr-311 116 18 with with ADP bjmsr-311 116 19 respect respect NOUN bjmsr-311 116 20 to to ADP bjmsr-311 116 21 j j NUM bjmsr-311 116 22 for for ADP bjmsr-311 116 23 all all DET bjmsr-311 116 24 j=1, j=1, NOUN bjmsr-311 116 25 ... ... PUNCT bjmsr-311 116 26 ,m ,m PUNCT bjmsr-311 116 27 and and CCONJ bjmsr-311 116 28 t. t. NOUN bjmsr-311 116 29 differentiating differentiating NOUN bjmsr-311 116 30 s s NOUN bjmsr-311 116 31 with with ADP bjmsr-311 116 32 respect respect NOUN bjmsr-311 116 33 to to ADP bjmsr-311 116 34 j j NUM bjmsr-311 116 35 for for ADP bjmsr-311 116 36 all all DET bjmsr-311 116 37 j=1, j=1, NOUN bjmsr-311 116 38 ... ... PUNCT bjmsr-311 116 39 ,m ,m PUNCT bjmsr-311 116 40 would would AUX bjmsr-311 116 41 give give VERB bjmsr-311 116 42 , , PUNCT bjmsr-311 116 43 δs δs NOUN bjmsr-311 116 44 t t PROPN bjmsr-311 116 45 n n CCONJ bjmsr-311 116 46 ─ ─ PROPN bjmsr-311 116 47 ─ ─ PROPN bjmsr-311 116 48 = = PUNCT bjmsr-311 116 49   NOUN bjmsr-311 116 50 xjh xjh NOUN bjmsr-311 117 1 + + CCONJ bjmsr-311 117 2   VERB bjmsr-311 117 3 xjh xjh PROPN bjmsr-311 117 4 j=1, j=1, NOUN bjmsr-311 117 5 ... ... PUNCT bjmsr-311 117 6 ,m ,m PUNCT bjmsr-311 117 7 ( ( PUNCT bjmsr-311 117 8 13 13 NUM bjmsr-311 117 9 ) ) PUNCT bjmsr-311 117 10 δßj δßj NOUN bjmsr-311 117 11 h=1 h=1 X bjmsr-311 117 12 h h NOUN bjmsr-311 117 13 = = VERB bjmsr-311 117 14 t+1 t+1 X bjmsr-311 117 15 in in ADP bjmsr-311 117 16 order order NOUN bjmsr-311 117 17 to to PART bjmsr-311 117 18 differentiate differentiate VERB bjmsr-311 117 19 s s PRON bjmsr-311 117 20 with with ADP bjmsr-311 117 21 respect respect NOUN bjmsr-311 117 22 to to PART bjmsr-311 117 23 discrete discrete ADJ bjmsr-311 117 24 domain domain NOUN bjmsr-311 117 25 variable variable NOUN bjmsr-311 117 26 t t NOUN bjmsr-311 117 27 we we PRON bjmsr-311 117 28 would would AUX bjmsr-311 117 29 have have VERB bjmsr-311 117 30 , , PUNCT bjmsr-311 117 31 (s (s NOUN bjmsr-311 117 32 ) ) PUNCT bjmsr-311 117 33 s[t+(t)]-s(t s[t+(t)]-s(t ADJ bjmsr-311 117 34 ) ) PUNCT bjmsr-311 117 35 copyright copyright NOUN bjmsr-311 118 1 © © PROPN bjmsr-311 118 2 cc cc PROPN bjmsr-311 118 3 - - PUNCT bjmsr-311 118 4 by by ADP bjmsr-311 118 5 - - PUNCT bjmsr-311 118 6 nc nc PROPN bjmsr-311 118 7 2019 2019 NUM bjmsr-311 118 8 , , PUNCT bjmsr-311 118 9 bjmsr bjmsr PROPN bjmsr-311 118 10 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 119 1 bangladesh bangladesh PROPN bjmsr-311 119 2 journal journal PROPN bjmsr-311 119 3 of of ADP bjmsr-311 119 4 multidisciplinary multidisciplinary ADJ bjmsr-311 119 5 scientific scientific ADJ bjmsr-311 119 6 research research NOUN bjmsr-311 119 7 vol vol NOUN bjmsr-311 119 8 . . PROPN bjmsr-311 119 9 1 1 NUM bjmsr-311 119 10 , , PUNCT bjmsr-311 119 11 no no INTJ bjmsr-311 119 12 . . NOUN bjmsr-311 119 13 1 1 NUM bjmsr-311 119 14 ; ; PUNCT bjmsr-311 119 15 2019 2019 NUM bjmsr-311 119 16 5 5 NUM bjmsr-311 119 17 ─ ─ ADJ bjmsr-311 119 18 ─ ─ PROPN bjmsr-311 119 19 ─ ─ PROPN bjmsr-311 119 20 = = SYM bjmsr-311 119 21 lim lim PROPN bjmsr-311 119 22 ─ ─ PROPN bjmsr-311 119 23 ─ ─ PROPN bjmsr-311 119 24 ─ ─ PROPN bjmsr-311 119 25 ─ ─ ADJ bjmsr-311 119 26 ─ ─ ADJ bjmsr-311 119 27 ─ ─ ADJ bjmsr-311 119 28 ─ ─ PROPN bjmsr-311 119 29 ─ ─ PROPN bjmsr-311 119 30 = = SYM bjmsr-311 119 31 s(t+1)-s(t s(t+1)-s(t PROPN bjmsr-311 119 32 ) ) PUNCT bjmsr-311 119 33 = = SYM bjmsr-311 119 34 (t (t PROPN bjmsr-311 119 35 ) ) PUNCT bjmsr-311 119 36 (t) (t) PROPN bjmsr-311 119 37 ─ ─ PROPN bjmsr-311 119 38 >1 >1 NOUN bjmsr-311 119 39 (t (t PROPN bjmsr-311 119 40 ) ) PUNCT bjmsr-311 120 1 t+1 t+1 NUM bjmsr-311 120 2 m m VERB bjmsr-311 120 3 n n ADV bjmsr-311 120 4 m m VERB bjmsr-311 120 5 t+1 t+1 PROPN bjmsr-311 120 6 m m PROPN bjmsr-311 120 7 n n NUM bjmsr-311 120 8 m m NOUN bjmsr-311 120 9 m m VERB bjmsr-311 120 10   ADJ bjmsr-311 120 11 ( ( PUNCT bjmsr-311 120 12 yh- yh- PROPN bjmsr-311 120 13 ßjxjh ßjxjh PROPN bjmsr-311 120 14 ) ) PUNCT bjmsr-311 120 15   PROPN bjmsr-311 120 16 ( ( PUNCT bjmsr-311 120 17 uh- uh- PROPN bjmsr-311 120 18 ßjxjh ßjxjh ADJ bjmsr-311 120 19 ) ) PUNCT bjmsr-311 120 20   PROPN bjmsr-311 120 21 ( ( PUNCT bjmsr-311 120 22 yh- yh- PROPN bjmsr-311 120 23 ßjxjh ßjxjh PART bjmsr-311 120 24 ) ) PUNCT bjmsr-311 121 1 + + CCONJ bjmsr-311 121 2   ADV bjmsr-311 121 3 ( ( PUNCT bjmsr-311 121 4 yh- yh- PROPN bjmsr-311 121 5 ßjxjh ßjxjh PROPN bjmsr-311 121 6 ) ) PUNCT bjmsr-311 121 7 = = SYM bjmsr-311 121 8 2(yt+1- 2(yt+1- NUM bjmsr-311 121 9 ßjxj ßjxj NOUN bjmsr-311 121 10 , , PUNCT bjmsr-311 121 11 t+1 t+1 PRON bjmsr-311 121 12 ) ) PUNCT bjmsr-311 121 13 = = SYM bjmsr-311 121 14 0 0 NUM bjmsr-311 121 15 ( ( PUNCT bjmsr-311 121 16 14 14 NUM bjmsr-311 121 17 ) ) PUNCT bjmsr-311 121 18 h=1 h=1 NOUN bjmsr-311 122 1 j=1 j=1 NOUN bjmsr-311 122 2 h h NOUN bjmsr-311 122 3 = = PROPN bjmsr-311 122 4 t+2 t+2 X bjmsr-311 122 5 j=1 j=1 NOUN bjmsr-311 123 1 h=1 h=1 X bjmsr-311 123 2 j=1 j=1 PROPN bjmsr-311 123 3 h h NOUN bjmsr-311 123 4 = = NOUN bjmsr-311 123 5 t+1 t+1 X bjmsr-311 123 6 j=1 j=1 NOUN bjmsr-311 124 1 j=1 j=1 PROPN bjmsr-311 124 2 m m VERB bjmsr-311 124 3 distinct distinct ADJ bjmsr-311 124 4 values value NOUN bjmsr-311 124 5 for for ADP bjmsr-311 124 6 t t PROPN bjmsr-311 124 7 can can AUX bjmsr-311 124 8 be be AUX bjmsr-311 124 9 computed compute VERB bjmsr-311 124 10 from from ADP bjmsr-311 124 11 ( ( PUNCT bjmsr-311 124 12 13 13 NUM bjmsr-311 124 13 ) ) PUNCT bjmsr-311 124 14 by by ADP bjmsr-311 124 15 using use VERB bjmsr-311 124 16 the the DET bjmsr-311 124 17 following follow VERB bjmsr-311 124 18 dkj dkj NOUN bjmsr-311 124 19 for for ADP bjmsr-311 124 20 each each DET bjmsr-311 124 21 explanatory explanatory ADJ bjmsr-311 124 22 variable variable NOUN bjmsr-311 124 23 . . PUNCT bjmsr-311 125 1 the the DET bjmsr-311 125 2 procedure procedure NOUN bjmsr-311 125 3 to to PART bjmsr-311 125 4 compute compute VERB bjmsr-311 125 5 t t PROPN bjmsr-311 125 6 is be AUX bjmsr-311 125 7 similar similar ADJ bjmsr-311 125 8 to to ADP bjmsr-311 125 9 what what PRON bjmsr-311 125 10 we we PRON bjmsr-311 125 11 did do AUX bjmsr-311 125 12 in in ADP bjmsr-311 125 13 ( ( PUNCT bjmsr-311 125 14 11 11 NUM bjmsr-311 125 15 ) ) PUNCT bjmsr-311 125 16 for for ADP bjmsr-311 125 17 the the DET bjmsr-311 125 18 one one NUM bjmsr-311 125 19 parameter parameter NOUN bjmsr-311 125 20 model model NOUN bjmsr-311 125 21 . . PUNCT bjmsr-311 126 1 k k PROPN bjmsr-311 126 2 n n PROPN bjmsr-311 126 3 dkj dkj VERB bjmsr-311 126 4 ≡ ≡ PROPN bjmsr-311 126 5   VERB bjmsr-311 126 6 xjh xjh NOUN bjmsr-311 126 7   PROPN bjmsr-311 126 8 xjh xjh PROPN bjmsr-311 126 9 j=1, j=1, NOUN bjmsr-311 126 10 ... ... PUNCT bjmsr-311 126 11 ,m ,m PUNCT bjmsr-311 126 12 ; ; PUNCT bjmsr-311 126 13 i=1, i=1, NOUN bjmsr-311 126 14 ... ... PUNCT bjmsr-311 126 15 ,n ,n PUNCT bjmsr-311 126 16 ( ( PUNCT bjmsr-311 126 17 15 15 NUM bjmsr-311 126 18 ) ) PUNCT bjmsr-311 126 19 h=1 h=1 NOUN bjmsr-311 126 20 h h NOUN bjmsr-311 126 21 = = VERB bjmsr-311 126 22 k+1 k+1 X bjmsr-311 126 23 it it PRON bjmsr-311 126 24 should should AUX bjmsr-311 126 25 be be AUX bjmsr-311 126 26 noted note VERB bjmsr-311 126 27 that that SCONJ bjmsr-311 126 28 these these PRON bjmsr-311 126 29 m m VERB bjmsr-311 126 30 values value NOUN bjmsr-311 126 31 for for ADP bjmsr-311 126 32 t t PROPN bjmsr-311 126 33 , , PUNCT bjmsr-311 126 34 all all PRON bjmsr-311 126 35 give give VERB bjmsr-311 126 36 a a DET bjmsr-311 126 37 unique unique ADJ bjmsr-311 126 38 value value NOUN bjmsr-311 126 39 for for ADP bjmsr-311 126 40 s s PRON bjmsr-311 126 41 in in ADP bjmsr-311 126 42 ( ( PUNCT bjmsr-311 126 43 12 12 NUM bjmsr-311 126 44 ) ) PUNCT bjmsr-311 126 45 , , PUNCT bjmsr-311 126 46 because because SCONJ bjmsr-311 126 47 all all PRON bjmsr-311 126 48 of of ADP bjmsr-311 126 49 the the DET bjmsr-311 126 50 errors error NOUN bjmsr-311 126 51 corresponding correspond VERB bjmsr-311 126 52 to to ADP bjmsr-311 126 53 these these DET bjmsr-311 126 54 t t PROPN bjmsr-311 126 55 's 's PART bjmsr-311 126 56 have have VERB bjmsr-311 126 57 zero zero NUM bjmsr-311 126 58 values value NOUN bjmsr-311 126 59 . . PUNCT bjmsr-311 127 1 this this PRON bjmsr-311 127 2 becomes become VERB bjmsr-311 127 3 clear clear ADJ bjmsr-311 127 4 by by ADP bjmsr-311 127 5 zero zero NUM bjmsr-311 127 6 residuals residual NOUN bjmsr-311 127 7 property property NOUN bjmsr-311 127 8 of of ADP bjmsr-311 127 9 the the DET bjmsr-311 127 10 l1 l1 PROPN bjmsr-311 127 11 norm norm PROPN bjmsr-311 127 12 regression regression NOUN bjmsr-311 127 13 that that SCONJ bjmsr-311 127 14 there there PRON bjmsr-311 127 15 exist exist VERB bjmsr-311 127 16 m m NUM bjmsr-311 127 17 points point NOUN bjmsr-311 127 18 on on ADP bjmsr-311 127 19 the the DET bjmsr-311 127 20 regression regression NOUN bjmsr-311 127 21 hyperplane hyperplane NOUN bjmsr-311 127 22 which which PRON bjmsr-311 127 23 have have VERB bjmsr-311 127 24 zero zero NUM bjmsr-311 127 25 residuals residual NOUN bjmsr-311 127 26 . . PUNCT bjmsr-311 128 1 in in ADP bjmsr-311 128 2 ( ( PUNCT bjmsr-311 128 3 12 12 NUM bjmsr-311 128 4 ) ) PUNCT bjmsr-311 128 5 , , PUNCT bjmsr-311 128 6 these these DET bjmsr-311 128 7 m m NOUN bjmsr-311 128 8 points point NOUN bjmsr-311 128 9 locate locate VERB bjmsr-311 128 10 sequentially sequentially ADV bjmsr-311 128 11 , , PUNCT bjmsr-311 128 12 because because SCONJ bjmsr-311 128 13 we we PRON bjmsr-311 128 14 had have AUX bjmsr-311 128 15 reordered reorder VERB bjmsr-311 128 16 observations observation NOUN bjmsr-311 128 17 in in ADP bjmsr-311 128 18 such such DET bjmsr-311 128 19 a a DET bjmsr-311 128 20 way way NOUN bjmsr-311 128 21 that that PRON bjmsr-311 128 22 , , PUNCT bjmsr-311 128 23 when when SCONJ bjmsr-311 128 24 h h NOUN bjmsr-311 128 25 increases increase VERB bjmsr-311 128 26 from from ADP bjmsr-311 128 27 one one NUM bjmsr-311 128 28 to to ADP bjmsr-311 128 29 n n CCONJ bjmsr-311 128 30 , , PUNCT bjmsr-311 128 31 the the DET bjmsr-311 128 32 errors error NOUN bjmsr-311 128 33 decrease decrease VERB bjmsr-311 128 34 from from ADP bjmsr-311 128 35 greatest great ADJ bjmsr-311 128 36 positive positive ADJ bjmsr-311 128 37 to to PART bjmsr-311 128 38 lowest low ADJ bjmsr-311 128 39 negative negative ADJ bjmsr-311 128 40 values value NOUN bjmsr-311 128 41 . . PUNCT bjmsr-311 129 1 so so ADV bjmsr-311 129 2 , , PUNCT bjmsr-311 129 3 these these DET bjmsr-311 129 4 m m ADJ bjmsr-311 129 5 zero zero NUM bjmsr-311 129 6 errors error NOUN bjmsr-311 129 7 will will AUX bjmsr-311 129 8 locate locate VERB bjmsr-311 129 9 one one NUM bjmsr-311 129 10 after after ADP bjmsr-311 129 11 another another PRON bjmsr-311 129 12 nearly nearly ADV bjmsr-311 129 13 in in ADP bjmsr-311 129 14 the the DET bjmsr-311 129 15 middle middle NOUN bjmsr-311 129 16 of of ADP bjmsr-311 129 17 n n NOUN bjmsr-311 129 18 elements element NOUN bjmsr-311 129 19 sequence sequence NOUN bjmsr-311 129 20 of of ADP bjmsr-311 129 21 ( ( PUNCT bjmsr-311 129 22 12 12 NUM bjmsr-311 129 23 ) ) PUNCT bjmsr-311 129 24 . . PUNCT bjmsr-311 130 1 corresponding correspond VERB bjmsr-311 130 2 to to ADP bjmsr-311 130 3 these these DET bjmsr-311 130 4 m m NOUN bjmsr-311 130 5 values value NOUN bjmsr-311 130 6 of of ADP bjmsr-311 130 7 t t PROPN bjmsr-311 130 8 , , PUNCT bjmsr-311 130 9 m m VERB bjmsr-311 130 10 observations observation NOUN bjmsr-311 130 11 are be AUX bjmsr-311 130 12 recognized recognize VERB bjmsr-311 130 13 . . PUNCT bjmsr-311 131 1 substitute substitute VERB bjmsr-311 131 2 the the DET bjmsr-311 131 3 values value NOUN bjmsr-311 131 4 of of ADP bjmsr-311 131 5 these these DET bjmsr-311 131 6 m m NOUN bjmsr-311 131 7 observations observation NOUN bjmsr-311 131 8 into into ADP bjmsr-311 131 9 ( ( PUNCT bjmsr-311 131 10 14 14 NUM bjmsr-311 131 11 ) ) PUNCT bjmsr-311 131 12 , , PUNCT bjmsr-311 131 13 m m NOUN bjmsr-311 131 14 equations equation NOUN bjmsr-311 131 15 are be AUX bjmsr-311 131 16 found find VERB bjmsr-311 131 17 which which PRON bjmsr-311 131 18 can can AUX bjmsr-311 131 19 be be AUX bjmsr-311 131 20 solved solve VERB bjmsr-311 131 21 simultaneously simultaneously ADV bjmsr-311 131 22 for for ADP bjmsr-311 131 23 m m VERB bjmsr-311 131 24 unknown unknown ADJ bjmsr-311 131 25 j j NOUN bjmsr-311 131 26 's 's PART bjmsr-311 131 27 . . PUNCT bjmsr-311 132 1 these these DET bjmsr-311 132 2 last last ADJ bjmsr-311 132 3 m m VERB bjmsr-311 132 4 equations equation NOUN bjmsr-311 132 5 again again ADV bjmsr-311 132 6 confirm confirm VERB bjmsr-311 132 7 the the DET bjmsr-311 132 8 abovecited abovecite VERB bjmsr-311 132 9 property property NOUN bjmsr-311 132 10 of of ADP bjmsr-311 132 11 the the DET bjmsr-311 132 12 l1 l1 PROPN bjmsr-311 132 13 norm norm PROPN bjmsr-311 132 14 regression regression PROPN bjmsr-311 132 15 . . PUNCT bjmsr-311 133 1 since since SCONJ bjmsr-311 133 2 for for ADP bjmsr-311 133 3 the the DET bjmsr-311 133 4 m m PROPN bjmsr-311 133 5 parameters parameter NOUN bjmsr-311 133 6 model model NOUN bjmsr-311 133 7 , , PUNCT bjmsr-311 133 8 the the DET bjmsr-311 133 9 ordering ordering NOUN bjmsr-311 133 10 of of ADP bjmsr-311 133 11 residuals residual NOUN bjmsr-311 133 12 before before ADP bjmsr-311 133 13 computing compute VERB bjmsr-311 133 14 optimal optimal ADJ bjmsr-311 133 15 values value NOUN bjmsr-311 133 16 of of ADP bjmsr-311 133 17 j j NOUN bjmsr-311 133 18 's 's PART bjmsr-311 133 19 is be AUX bjmsr-311 133 20 not not PART bjmsr-311 133 21 possible possible ADJ bjmsr-311 133 22 , , PUNCT bjmsr-311 133 23 another another DET bjmsr-311 133 24 device device NOUN bjmsr-311 133 25 should should AUX bjmsr-311 133 26 be be AUX bjmsr-311 133 27 adopted adopt VERB bjmsr-311 133 28 to to PART bjmsr-311 133 29 compute compute VERB bjmsr-311 133 30 the the DET bjmsr-311 133 31 l1 l1 PROPN bjmsr-311 133 32 norm norm NOUN bjmsr-311 133 33 estimates estimate NOUN bjmsr-311 133 34 of of ADP bjmsr-311 133 35 the the DET bjmsr-311 133 36 multiple multiple ADJ bjmsr-311 133 37 linear linear PROPN bjmsr-311 133 38 regression regression NOUN bjmsr-311 133 39 parameters parameter NOUN bjmsr-311 133 40 . . PUNCT bjmsr-311 134 1 3 3 X bjmsr-311 134 2 . . X bjmsr-311 134 3 unrestricted unrestricted ADJ bjmsr-311 134 4 simple simple ADJ bjmsr-311 134 5 linear linear ADJ bjmsr-311 134 6 regression regression NOUN bjmsr-311 134 7 to to PART bjmsr-311 134 8 find find VERB bjmsr-311 134 9 the the DET bjmsr-311 134 10 l1 l1 PROPN bjmsr-311 134 11 norm norm NOUN bjmsr-311 134 12 estimates estimate NOUN bjmsr-311 134 13 of of ADP bjmsr-311 134 14 { { PUNCT bjmsr-311 134 15 j j NOUN bjmsr-311 134 16 , , PUNCT bjmsr-311 134 17 j=1, j=1, NOUN bjmsr-311 134 18 ... ... PUNCT bjmsr-311 134 19 ,m ,m PUNCT bjmsr-311 134 20 } } PUNCT bjmsr-311 134 21 for for ADP bjmsr-311 134 22 the the DET bjmsr-311 134 23 model model NOUN bjmsr-311 134 24 ( ( PUNCT bjmsr-311 134 25 1 1 NUM bjmsr-311 134 26 ) ) PUNCT bjmsr-311 134 27 , , PUNCT bjmsr-311 134 28 we we PRON bjmsr-311 134 29 shall shall AUX bjmsr-311 134 30 try try VERB bjmsr-311 134 31 to to PART bjmsr-311 134 32 propose propose VERB bjmsr-311 134 33 algorithms algorithm NOUN bjmsr-311 134 34 to to PART bjmsr-311 134 35 search search VERB bjmsr-311 134 36 for for ADP bjmsr-311 134 37 those those DET bjmsr-311 134 38 observations observation NOUN bjmsr-311 134 39 on on ADP bjmsr-311 134 40 the the DET bjmsr-311 134 41 optimal optimal ADJ bjmsr-311 134 42 regression regression NOUN bjmsr-311 134 43 hyperplane hyperplane NOUN bjmsr-311 134 44 . . PUNCT bjmsr-311 135 1 for for ADP bjmsr-311 135 2 m=2 m=2 PROPN bjmsr-311 135 3 and and CCONJ bjmsr-311 135 4 x1i=0 x1i=0 PROPN bjmsr-311 135 5 , , PUNCT bjmsr-311 135 6 i=1, i=1, NOUN bjmsr-311 135 7 ... ... PUNCT bjmsr-311 135 8 ,n ,n PUNCT bjmsr-311 135 9 ; ; PUNCT bjmsr-311 135 10 ( ( PUNCT bjmsr-311 135 11 1 1 X bjmsr-311 135 12 ) ) PUNCT bjmsr-311 135 13 reduces reduce VERB bjmsr-311 135 14 to to PART bjmsr-311 135 15 restricted restricted VERB bjmsr-311 135 16 simple simple ADJ bjmsr-311 135 17 linear linear ADJ bjmsr-311 135 18 regression regression NOUN bjmsr-311 135 19 with with ADP bjmsr-311 135 20 only only ADV bjmsr-311 135 21 one one NUM bjmsr-311 135 22 parameter parameter NOUN bjmsr-311 135 23 . . PUNCT bjmsr-311 136 1 the the DET bjmsr-311 136 2 l1 l1 PROPN bjmsr-311 136 3 norm norm NOUN bjmsr-311 136 4 estimate estimate NOUN bjmsr-311 136 5 of of ADP bjmsr-311 136 6 the the DET bjmsr-311 136 7 slope slope NOUN bjmsr-311 136 8 2 2 NOUN bjmsr-311 136 9 for for ADP bjmsr-311 136 10 the the DET bjmsr-311 136 11 simple simple ADJ bjmsr-311 136 12 model model NOUN bjmsr-311 136 13 can can AUX bjmsr-311 136 14 be be AUX bjmsr-311 136 15 obtained obtain VERB bjmsr-311 136 16 by by ADP bjmsr-311 136 17 the the DET bjmsr-311 136 18 algorithm algorithm NOUN bjmsr-311 136 19 given give VERB bjmsr-311 136 20 in in ADP bjmsr-311 136 21 the the DET bjmsr-311 136 22 previous previous ADJ bjmsr-311 136 23 sections section NOUN bjmsr-311 136 24 . . PUNCT bjmsr-311 137 1 let let VERB bjmsr-311 137 2 us we PRON bjmsr-311 137 3 now now ADV bjmsr-311 137 4 consider consider VERB bjmsr-311 137 5 a a DET bjmsr-311 137 6 simple simple ADJ bjmsr-311 137 7 unrestricted unrestricted ADJ bjmsr-311 137 8 linear linear NOUN bjmsr-311 137 9 model model NOUN bjmsr-311 137 10 in in ADP bjmsr-311 137 11 which which PRON bjmsr-311 137 12 m=2 m=2 PROPN bjmsr-311 137 13 and and CCONJ bjmsr-311 137 14 x1i=1 x1i=1 PUNCT bjmsr-311 137 15 for for ADP bjmsr-311 137 16 all all DET bjmsr-311 137 17 i=1, i=1, NOUN bjmsr-311 137 18 ... ... PUNCT bjmsr-311 137 19 ,n ,n NOUN bjmsr-311 137 20 ; ; PUNCT bjmsr-311 137 21 namely namely ADV bjmsr-311 137 22 , , PUNCT bjmsr-311 137 23 yi yi PROPN bjmsr-311 137 24 = = PUNCT bjmsr-311 137 25 ß1 ß1 PROPN bjmsr-311 137 26 + + CCONJ bjmsr-311 137 27 ß2x2i ß2x2i SYM bjmsr-311 137 28 + + NUM bjmsr-311 137 29 ui ui NOUN bjmsr-311 137 30 ( ( PUNCT bjmsr-311 137 31 16 16 NUM bjmsr-311 137 32 ) ) PUNCT bjmsr-311 137 33 3.1 3.1 NUM bjmsr-311 137 34 algorithm algorithm NOUN bjmsr-311 137 35 1 1 NUM bjmsr-311 137 36 for for ADP bjmsr-311 137 37 the the DET bjmsr-311 137 38 model model NOUN bjmsr-311 137 39 given give VERB bjmsr-311 137 40 in in ADP bjmsr-311 137 41 ( ( PUNCT bjmsr-311 137 42 16 16 NUM bjmsr-311 137 43 ) ) PUNCT bjmsr-311 137 44 , , PUNCT bjmsr-311 137 45 the the DET bjmsr-311 137 46 l1 l1 PROPN bjmsr-311 137 47 norm norm VERB bjmsr-311 137 48 objective objective ADJ bjmsr-311 137 49 function function NOUN bjmsr-311 137 50 s s VERB bjmsr-311 137 51 to to PART bjmsr-311 137 52 be be AUX bjmsr-311 137 53 minimized minimize VERB bjmsr-311 137 54 will will AUX bjmsr-311 137 55 be be AUX bjmsr-311 137 56 , , PUNCT bjmsr-311 137 57 n n PROPN bjmsr-311 137 58 s s NOUN bjmsr-311 137 59 = = PUNCT bjmsr-311 137 60   ADJ bjmsr-311 137 61 │ │ NUM bjmsr-311 137 62 yi yi NOUN bjmsr-311 137 63 ß1 ß1 NOUN bjmsr-311 137 64 ß2x2i ß2x2i NUM bjmsr-311 137 65 │ │ X bjmsr-311 137 66 ( ( PUNCT bjmsr-311 137 67 17 17 NUM bjmsr-311 137 68 ) ) PUNCT bjmsr-311 137 69 i=1 i=1 VERB bjmsr-311 137 70 let let VERB bjmsr-311 137 71 k1 k1 PROPN bjmsr-311 137 72 denote denote VERB bjmsr-311 137 73 a a DET bjmsr-311 137 74 subscript subscript NOUN bjmsr-311 137 75 which which PRON bjmsr-311 137 76 belongs belong VERB bjmsr-311 137 77 to to ADP bjmsr-311 137 78 the the DET bjmsr-311 137 79 range range NOUN bjmsr-311 137 80 of of ADP bjmsr-311 137 81 one one NUM bjmsr-311 137 82 to to ADP bjmsr-311 137 83 n n CCONJ bjmsr-311 137 84 , , PUNCT bjmsr-311 137 85 and and CCONJ bjmsr-311 137 86 assume assume VERB bjmsr-311 137 87 that that SCONJ bjmsr-311 137 88 k1 k1 NOUN bjmsr-311 137 89 th th X bjmsr-311 137 90 observation observation NOUN bjmsr-311 137 91 ( ( PUNCT bjmsr-311 137 92 yk1,x2k1 yk1,x2k1 PROPN bjmsr-311 137 93 ) ) PUNCT bjmsr-311 137 94 is be AUX bjmsr-311 137 95 a a DET bjmsr-311 137 96 candidate candidate NOUN bjmsr-311 137 97 to to PART bjmsr-311 137 98 be be AUX bjmsr-311 137 99 on on ADP bjmsr-311 137 100 the the DET bjmsr-311 137 101 regression regression NOUN bjmsr-311 137 102 line line NOUN bjmsr-311 137 103 . . PUNCT bjmsr-311 138 1 if if SCONJ bjmsr-311 138 2 this this PRON bjmsr-311 138 3 is be AUX bjmsr-311 138 4 the the DET bjmsr-311 138 5 case case NOUN bjmsr-311 138 6 , , PUNCT bjmsr-311 138 7 then then ADV bjmsr-311 138 8 uk1=0 uk1=0 ADJ bjmsr-311 138 9 and and CCONJ bjmsr-311 138 10 we we PRON bjmsr-311 138 11 can can AUX bjmsr-311 138 12 transfer transfer VERB bjmsr-311 138 13 the the DET bjmsr-311 138 14 origin origin NOUN bjmsr-311 138 15 of of ADP bjmsr-311 138 16 yxx2 yxx2 PROPN bjmsr-311 138 17 coordinates coordinate VERB bjmsr-311 138 18 to to ADP bjmsr-311 138 19 the the DET bjmsr-311 138 20 point point NOUN bjmsr-311 138 21 ( ( PUNCT bjmsr-311 138 22 yk1,x2k1 yk1,x2k1 PROPN bjmsr-311 138 23 ) ) PUNCT bjmsr-311 138 24 without without ADP bjmsr-311 138 25 any any DET bjmsr-311 138 26 loss loss NOUN bjmsr-311 138 27 . . PUNCT bjmsr-311 139 1 for for ADP bjmsr-311 139 2 this this PRON bjmsr-311 139 3 , , PUNCT bjmsr-311 139 4 we we PRON bjmsr-311 139 5 should should AUX bjmsr-311 139 6 rewrite rewrite VERB bjmsr-311 139 7 all all DET bjmsr-311 139 8 observations observation NOUN bjmsr-311 139 9 as as ADP bjmsr-311 139 10 deviates deviate VERB bjmsr-311 139 11 from from ADP bjmsr-311 139 12 the the DET bjmsr-311 139 13 point point NOUN bjmsr-311 139 14 ( ( PUNCT bjmsr-311 139 15 yk1,x2k1 yk1,x2k1 PROPN bjmsr-311 139 16 ) ) PUNCT bjmsr-311 139 17 , , PUNCT bjmsr-311 139 18 yi yi PROPN bjmsr-311 139 19 k1 k1 PROPN bjmsr-311 139 20 = = SYM bjmsr-311 139 21 yi yi PROPN bjmsr-311 139 22 yk1 yk1 PROPN bjmsr-311 139 23 , , PUNCT bjmsr-311 139 24 x2i x2i PROPN bjmsr-311 139 25 k1= k1= PROPN bjmsr-311 139 26 x2i x2i PUNCT bjmsr-311 139 27 x2k1 x2k1 PROPN bjmsr-311 139 28 i=1, i=1, PROPN bjmsr-311 139 29 ... ... PUNCT bjmsr-311 139 30 ,n ,n PUNCT bjmsr-311 139 31 ( ( PUNCT bjmsr-311 139 32 18 18 NUM bjmsr-311 139 33 ) ) PUNCT bjmsr-311 139 34 where where SCONJ bjmsr-311 139 35 the the DET bjmsr-311 139 36 terms term NOUN bjmsr-311 139 37 with with ADP bjmsr-311 139 38 superscripts superscripts PROPN bjmsr-311 139 39 k1 k1 PROPN bjmsr-311 139 40 denote denote VERB bjmsr-311 139 41 deviated deviate VERB bjmsr-311 139 42 values value NOUN bjmsr-311 139 43 . . PUNCT bjmsr-311 140 1 rearrange rearrange VERB bjmsr-311 140 2 the the DET bjmsr-311 140 3 terms term NOUN bjmsr-311 140 4 ; ; PUNCT bjmsr-311 140 5 yi yi PROPN bjmsr-311 140 6 = = PROPN bjmsr-311 140 7 yi yi PROPN bjmsr-311 140 8 k1 k1 NOUN bjmsr-311 140 9 + + CCONJ bjmsr-311 140 10 yk1 yk1 PROPN bjmsr-311 140 11 , , PUNCT bjmsr-311 140 12 x2i x2i PROPN bjmsr-311 141 1 = = PROPN bjmsr-311 141 2 x2i x2i PROPN bjmsr-311 141 3 k1 k1 PROPN bjmsr-311 141 4 + + CCONJ bjmsr-311 141 5 x2k1 x2k1 PROPN bjmsr-311 141 6 i=1, i=1, PROPN bjmsr-311 141 7 ... ... PUNCT bjmsr-311 141 8 ,n ,n PUNCT bjmsr-311 141 9 ( ( PUNCT bjmsr-311 141 10 19 19 NUM bjmsr-311 141 11 ) ) PUNCT bjmsr-311 141 12 i=1, i=1, NOUN bjmsr-311 141 13 ... ... PUNCT bjmsr-311 141 14 ,n ,n PUNCT bjmsr-311 141 15 now now ADV bjmsr-311 141 16 , , PUNCT bjmsr-311 141 17 substitute substitute NOUN bjmsr-311 141 18 ( ( PUNCT bjmsr-311 141 19 19 19 NUM bjmsr-311 141 20 ) ) PUNCT bjmsr-311 141 21 into into ADP bjmsr-311 141 22 ( ( PUNCT bjmsr-311 141 23 17 17 NUM bjmsr-311 141 24 ) ) PUNCT bjmsr-311 141 25 , , PUNCT bjmsr-311 141 26 then then ADV bjmsr-311 141 27 , , PUNCT bjmsr-311 141 28 our our PRON bjmsr-311 141 29 l1 l1 PROPN bjmsr-311 141 30 norm norm NOUN bjmsr-311 141 31 minimization minimization NOUN bjmsr-311 141 32 problem problem NOUN bjmsr-311 141 33 can can AUX bjmsr-311 141 34 be be AUX bjmsr-311 141 35 redefined redefine VERB bjmsr-311 141 36 as as ADP bjmsr-311 141 37 , , PUNCT bjmsr-311 141 38 n n PRON bjmsr-311 141 39 min min NOUN bjmsr-311 141 40 : : PUNCT bjmsr-311 141 41 sk1 sk1 PROPN bjmsr-311 141 42 = = PUNCT bjmsr-311 141 43   PROPN bjmsr-311 141 44 |yi |yi NUM bjmsr-311 141 45 k1-2x2i k1-2x2i PROPN bjmsr-311 141 46 k1 k1 PROPN bjmsr-311 141 47 + + CCONJ bjmsr-311 141 48 ( ( PUNCT bjmsr-311 141 49 yk1-1-2x2k1)| yk1-1-2x2k1)| X bjmsr-311 141 50 ( ( PUNCT bjmsr-311 141 51 20 20 NUM bjmsr-311 141 52 ) ) PUNCT bjmsr-311 141 53 1,2 1,2 NOUN bjmsr-311 141 54 i=1 i=1 PRON bjmsr-311 142 1 copyright copyright NOUN bjmsr-311 142 2 © © PROPN bjmsr-311 142 3 cc cc PROPN bjmsr-311 142 4 - - PUNCT bjmsr-311 142 5 by by ADP bjmsr-311 142 6 - - PUNCT bjmsr-311 142 7 nc nc PROPN bjmsr-311 142 8 2019 2019 NUM bjmsr-311 142 9 , , PUNCT bjmsr-311 142 10 bjmsr bjmsr PROPN bjmsr-311 142 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 143 1 bangladesh bangladesh PROPN bjmsr-311 143 2 journal journal PROPN bjmsr-311 143 3 of of ADP bjmsr-311 143 4 multidisciplinary multidisciplinary ADJ bjmsr-311 143 5 scientific scientific ADJ bjmsr-311 143 6 research research NOUN bjmsr-311 143 7 vol vol NOUN bjmsr-311 143 8 . . PROPN bjmsr-311 143 9 1 1 NUM bjmsr-311 143 10 , , PUNCT bjmsr-311 143 11 no no INTJ bjmsr-311 143 12 . . NOUN bjmsr-311 143 13 1 1 NUM bjmsr-311 143 14 ; ; PUNCT bjmsr-311 143 15 2019 2019 NUM bjmsr-311 143 16 6 6 NUM bjmsr-311 143 17 since since SCONJ bjmsr-311 143 18 we we PRON bjmsr-311 143 19 assumed assume VERB bjmsr-311 143 20 that that SCONJ bjmsr-311 143 21 the the DET bjmsr-311 143 22 k1th k1th PUNCT bjmsr-311 143 23 observation observation NOUN bjmsr-311 143 24 is be AUX bjmsr-311 143 25 on on ADP bjmsr-311 143 26 the the DET bjmsr-311 143 27 regression regression NOUN bjmsr-311 143 28 line line NOUN bjmsr-311 143 29 , , PUNCT bjmsr-311 143 30 the the DET bjmsr-311 143 31 expression expression NOUN bjmsr-311 143 32 yk1-1-2x2k1=0 yk1-1-2x2k1=0 PROPN bjmsr-311 143 33 . . PUNCT bjmsr-311 144 1 thus thus ADV bjmsr-311 144 2 ( ( PUNCT bjmsr-311 144 3 20 20 NUM bjmsr-311 144 4 ) ) PUNCT bjmsr-311 144 5 reduces reduce VERB bjmsr-311 144 6 to to ADP bjmsr-311 144 7 , , PUNCT bjmsr-311 144 8 n n PRON bjmsr-311 144 9 min min PROPN bjmsr-311 144 10 : : PUNCT bjmsr-311 144 11 sk1 sk1 PROPN bjmsr-311 144 12 = = PUNCT bjmsr-311 144 13   PROPN bjmsr-311 144 14 |yik1 |yik1 PROPN bjmsr-311 144 15 2x2i 2x2i PROPN bjmsr-311 144 16 k1| k1| PROPN bjmsr-311 144 17 ( ( PUNCT bjmsr-311 144 18 21 21 NUM bjmsr-311 144 19 ) ) PUNCT bjmsr-311 144 20 2 2 NOUN bjmsr-311 144 21 i=1 i=1 X bjmsr-311 144 22 the the DET bjmsr-311 144 23 solution solution NOUN bjmsr-311 144 24 of of ADP bjmsr-311 144 25 the the DET bjmsr-311 144 26 optimization optimization NOUN bjmsr-311 144 27 problem problem NOUN bjmsr-311 144 28 ( ( PUNCT bjmsr-311 144 29 21 21 NUM bjmsr-311 144 30 ) ) PUNCT bjmsr-311 144 31 , , PUNCT bjmsr-311 144 32 is be AUX bjmsr-311 144 33 the the DET bjmsr-311 144 34 same same ADJ bjmsr-311 144 35 as as ADP bjmsr-311 144 36 the the DET bjmsr-311 144 37 one one NOUN bjmsr-311 144 38 described describe VERB bjmsr-311 144 39 before before ADV bjmsr-311 144 40 for for ADP bjmsr-311 144 41 one one NUM bjmsr-311 144 42 parameter parameter NOUN bjmsr-311 144 43 linear linear PROPN bjmsr-311 144 44 model model NOUN bjmsr-311 144 45 . . PUNCT bjmsr-311 145 1 note note VERB bjmsr-311 145 2 that that SCONJ bjmsr-311 145 3 when when SCONJ bjmsr-311 145 4 uk1=0 uk1=0 ADJ bjmsr-311 145 5 , , PUNCT bjmsr-311 145 6 then then ADV bjmsr-311 145 7 the the DET bjmsr-311 145 8 minimum minimum ADJ bjmsr-311 145 9 value value NOUN bjmsr-311 145 10 of of ADP bjmsr-311 145 11 ( ( PUNCT bjmsr-311 145 12 21 21 NUM bjmsr-311 145 13 ) ) PUNCT bjmsr-311 145 14 is be AUX bjmsr-311 145 15 equal equal ADJ bjmsr-311 145 16 to to ADP bjmsr-311 145 17 the the DET bjmsr-311 145 18 minimum minimum ADJ bjmsr-311 145 19 value value NOUN bjmsr-311 145 20 of of ADP bjmsr-311 145 21 ( ( PUNCT bjmsr-311 145 22 17 17 NUM bjmsr-311 145 23 ) ) PUNCT bjmsr-311 145 24 . . PUNCT bjmsr-311 146 1 let let VERB bjmsr-311 146 2 2 2 NOUN bjmsr-311 146 3 derived derive VERB bjmsr-311 146 4 by by ADP bjmsr-311 146 5 minimizing minimize VERB bjmsr-311 146 6 ( ( PUNCT bjmsr-311 146 7 21 21 NUM bjmsr-311 146 8 ) ) PUNCT bjmsr-311 146 9 be be AUX bjmsr-311 146 10 denoted denote VERB bjmsr-311 146 11 by by ADP bjmsr-311 146 12 2 2 ADJ bjmsr-311 146 13 k1 k1 PROPN bjmsr-311 146 14 . . PUNCT bjmsr-311 147 1 by by ADP bjmsr-311 147 2 changing change VERB bjmsr-311 147 3 k1 k1 NOUN bjmsr-311 147 4 from from ADP bjmsr-311 147 5 one one NUM bjmsr-311 147 6 to to ADP bjmsr-311 147 7 n n NOUN bjmsr-311 147 8 and and CCONJ bjmsr-311 147 9 minimizing minimize VERB bjmsr-311 147 10 ( ( PUNCT bjmsr-311 147 11 21 21 NUM bjmsr-311 147 12 ) ) PUNCT bjmsr-311 147 13 , , PUNCT bjmsr-311 147 14 2 2 VERB bjmsr-311 147 15 1, 1, NUM bjmsr-311 147 16 ... ... PUNCT bjmsr-311 147 17 ,2 ,2 PUNCT bjmsr-311 147 18 n n PRON bjmsr-311 147 19 are be AUX bjmsr-311 147 20 attained attain VERB bjmsr-311 147 21 accordingly accordingly ADV bjmsr-311 147 22 . . PUNCT bjmsr-311 148 1 now now ADV bjmsr-311 148 2 the the DET bjmsr-311 148 3 question question NOUN bjmsr-311 148 4 is be AUX bjmsr-311 148 5 : : PUNCT bjmsr-311 148 6 what what DET bjmsr-311 148 7 value value NOUN bjmsr-311 148 8 of of ADP bjmsr-311 148 9 k1 k1 NOUN bjmsr-311 148 10 minimizes minimize NOUN bjmsr-311 148 11 ( ( PUNCT bjmsr-311 148 12 17 17 NUM bjmsr-311 148 13 ) ) PUNCT bjmsr-311 148 14 ? ? PUNCT bjmsr-311 149 1 in in ADP bjmsr-311 149 2 other other ADJ bjmsr-311 149 3 words word NOUN bjmsr-311 149 4 , , PUNCT bjmsr-311 149 5 which which DET bjmsr-311 149 6 observations observation NOUN bjmsr-311 149 7 are be AUX bjmsr-311 149 8 on on ADP bjmsr-311 149 9 the the DET bjmsr-311 149 10 optimal optimal ADJ bjmsr-311 149 11 regression regression NOUN bjmsr-311 149 12 line line NOUN bjmsr-311 149 13 ? ? PUNCT bjmsr-311 150 1 note note VERB bjmsr-311 150 2 that that SCONJ bjmsr-311 150 3 in in ADP bjmsr-311 150 4 the the DET bjmsr-311 150 5 two two NUM bjmsr-311 150 6 parameters parameter NOUN bjmsr-311 150 7 l1 l1 PROPN bjmsr-311 150 8 norm norm PROPN bjmsr-311 150 9 linear linear PROPN bjmsr-311 150 10 model model PROPN bjmsr-311 150 11 , , PUNCT bjmsr-311 150 12 there there PRON bjmsr-311 150 13 exists exist VERB bjmsr-311 150 14 at at ADP bjmsr-311 150 15 least least ADV bjmsr-311 150 16 two two NUM bjmsr-311 150 17 observations observation NOUN bjmsr-311 150 18 with with ADP bjmsr-311 150 19 zero zero NUM bjmsr-311 150 20 errors error NOUN bjmsr-311 150 21 . . PUNCT bjmsr-311 151 1 transferring transfer VERB bjmsr-311 151 2 of of ADP bjmsr-311 151 3 yxx2 yxx2 PROPN bjmsr-311 151 4 coordinates coordinate NOUN bjmsr-311 151 5 to to ADP bjmsr-311 151 6 both both DET bjmsr-311 151 7 these these DET bjmsr-311 151 8 points point NOUN bjmsr-311 151 9 does do AUX bjmsr-311 151 10 not not PART bjmsr-311 151 11 change change VERB bjmsr-311 151 12 the the DET bjmsr-311 151 13 minimum minimum NOUN bjmsr-311 151 14 of of ADP bjmsr-311 151 15 ( ( PUNCT bjmsr-311 151 16 17 17 NUM bjmsr-311 151 17 ) ) PUNCT bjmsr-311 151 18 . . PUNCT bjmsr-311 152 1 suppose suppose VERB bjmsr-311 152 2 p p X bjmsr-311 152 3 th th X bjmsr-311 152 4 and and CCONJ bjmsr-311 152 5 qth qth NOUN bjmsr-311 152 6 are be AUX bjmsr-311 152 7 those those DET bjmsr-311 152 8 observations observation NOUN bjmsr-311 152 9 on on ADP bjmsr-311 152 10 the the DET bjmsr-311 152 11 regression regression NOUN bjmsr-311 152 12 line line NOUN bjmsr-311 152 13 , , PUNCT bjmsr-311 152 14 thus thus ADV bjmsr-311 152 15 , , PUNCT bjmsr-311 152 16 up up ADV bjmsr-311 153 1 = = SYM bjmsr-311 153 2 yp yp PROPN bjmsr-311 153 3 1 1 NOUN bjmsr-311 154 1 2x2p 2x2p NOUN bjmsr-311 154 2 = = SYM bjmsr-311 154 3 0 0 NUM bjmsr-311 154 4 , , PUNCT bjmsr-311 154 5 uq uq NOUN bjmsr-311 154 6 = = PROPN bjmsr-311 154 7 yq yq PROPN bjmsr-311 154 8 1 1 NOUN bjmsr-311 154 9 2x2q 2x2q ADJ bjmsr-311 154 10 = = SYM bjmsr-311 154 11 0 0 NUM bjmsr-311 154 12 ( ( PUNCT bjmsr-311 154 13 22 22 NUM bjmsr-311 154 14 ) ) PUNCT bjmsr-311 154 15 rewriting rewrite VERB bjmsr-311 154 16 ( ( PUNCT bjmsr-311 154 17 18 18 NUM bjmsr-311 154 18 ) ) PUNCT bjmsr-311 154 19 and and CCONJ bjmsr-311 154 20 ( ( PUNCT bjmsr-311 154 21 19 19 NUM bjmsr-311 154 22 ) ) PUNCT bjmsr-311 154 23 for for ADP bjmsr-311 154 24 k1 k1 NOUN bjmsr-311 154 25 = = SYM bjmsr-311 154 26 p p NOUN bjmsr-311 154 27 , , PUNCT bjmsr-311 154 28 q q NOUN bjmsr-311 154 29 and and CCONJ bjmsr-311 154 30 substituting substitute VERB bjmsr-311 154 31 them they PRON bjmsr-311 154 32 into into ADP bjmsr-311 154 33 ( ( PUNCT bjmsr-311 154 34 21 21 NUM bjmsr-311 154 35 ) ) PUNCT bjmsr-311 154 36 , , PUNCT bjmsr-311 154 37 yields yield NOUN bjmsr-311 154 38 , , PUNCT bjmsr-311 154 39 n n PRON bjmsr-311 154 40 sp sp ADP bjmsr-311 154 41 = = PUNCT bjmsr-311 154 42   NOUN bjmsr-311 154 43 |yi |yi NUM bjmsr-311 154 44 p p PROPN bjmsr-311 154 45 2x2i 2x2i PROPN bjmsr-311 154 46 p| p| PROPN bjmsr-311 154 47 ( ( PUNCT bjmsr-311 154 48 23 23 NUM bjmsr-311 154 49 ) ) PUNCT bjmsr-311 154 50 i=1 i=1 PROPN bjmsr-311 154 51 n n CCONJ bjmsr-311 154 52 sq sq ADJ bjmsr-311 154 53 = = PUNCT bjmsr-311 154 54   NOUN bjmsr-311 154 55 |yi |yi PRON bjmsr-311 154 56 q q PROPN bjmsr-311 154 57 2x2i 2x2i PROPN bjmsr-311 154 58 q| q| PROPN bjmsr-311 154 59 ( ( PUNCT bjmsr-311 154 60 24 24 NUM bjmsr-311 154 61 ) ) PUNCT bjmsr-311 154 62 i=1 i=1 VERB bjmsr-311 154 63 using use VERB bjmsr-311 154 64 ( ( PUNCT bjmsr-311 154 65 18 18 NUM bjmsr-311 154 66 ) ) PUNCT bjmsr-311 154 67 and and CCONJ bjmsr-311 154 68 rewriting rewrite VERB bjmsr-311 154 69 ( ( PUNCT bjmsr-311 154 70 23 23 NUM bjmsr-311 154 71 ) ) PUNCT bjmsr-311 154 72 and and CCONJ bjmsr-311 154 73 ( ( PUNCT bjmsr-311 154 74 24 24 NUM bjmsr-311 154 75 ) ) PUNCT bjmsr-311 154 76 , , PUNCT bjmsr-311 154 77 it it PRON bjmsr-311 154 78 is be AUX bjmsr-311 154 79 shown show VERB bjmsr-311 154 80 that that SCONJ bjmsr-311 154 81 sp sp NOUN bjmsr-311 154 82 is be AUX bjmsr-311 154 83 equal equal ADJ bjmsr-311 154 84 to to ADP bjmsr-311 154 85 sq sq PROPN bjmsr-311 154 86 , , PUNCT bjmsr-311 154 87 n n PRON bjmsr-311 154 88 sp sp ADP bjmsr-311 154 89 = = PUNCT bjmsr-311 154 90   ADJ bjmsr-311 154 91 |yi-2x2i |yi-2x2i PROPN bjmsr-311 154 92 ( ( PUNCT bjmsr-311 154 93 yp-2x2p)| yp-2x2p)| NUM bjmsr-311 154 94 ( ( PUNCT bjmsr-311 154 95 25 25 NUM bjmsr-311 154 96 ) ) PUNCT bjmsr-311 154 97 i=1 i=1 PROPN bjmsr-311 154 98 n n CCONJ bjmsr-311 155 1 sq sq ADJ bjmsr-311 155 2 = = PUNCT bjmsr-311 155 3   ADJ bjmsr-311 155 4 |yi-2x2i |yi-2x2i NOUN bjmsr-311 155 5 ( ( PUNCT bjmsr-311 155 6 yq-2x2q)| yq-2x2q)| NUM bjmsr-311 155 7 ( ( PUNCT bjmsr-311 155 8 26 26 NUM bjmsr-311 155 9 ) ) PUNCT bjmsr-311 155 10 i=1 i=1 NOUN bjmsr-311 155 11 sp sp NOUN bjmsr-311 155 12 is be AUX bjmsr-311 155 13 equal equal ADJ bjmsr-311 155 14 to to ADP bjmsr-311 155 15 sq sq VERB bjmsr-311 155 16 if if SCONJ bjmsr-311 156 1 and and CCONJ bjmsr-311 156 2 only only ADV bjmsr-311 156 3 if if SCONJ bjmsr-311 156 4 the the DET bjmsr-311 156 5 two two NUM bjmsr-311 156 6 parentheses parenthesis NOUN bjmsr-311 156 7 inside inside ADP bjmsr-311 156 8 the the DET bjmsr-311 156 9 absolute absolute ADJ bjmsr-311 156 10 value value NOUN bjmsr-311 156 11 signs sign NOUN bjmsr-311 156 12 of of ADP bjmsr-311 156 13 ( ( PUNCT bjmsr-311 156 14 25 25 NUM bjmsr-311 156 15 ) ) PUNCT bjmsr-311 156 16 and and CCONJ bjmsr-311 156 17 ( ( PUNCT bjmsr-311 156 18 26 26 NUM bjmsr-311 156 19 ) ) PUNCT bjmsr-311 156 20 are be AUX bjmsr-311 156 21 equal equal ADJ bjmsr-311 156 22 . . PUNCT bjmsr-311 157 1 this this PRON bjmsr-311 157 2 can can AUX bjmsr-311 157 3 be be AUX bjmsr-311 157 4 concluded conclude VERB bjmsr-311 157 5 by by ADP bjmsr-311 157 6 solving solve VERB bjmsr-311 157 7 the the DET bjmsr-311 157 8 two two NUM bjmsr-311 157 9 equations equation NOUN bjmsr-311 157 10 of of ADP bjmsr-311 157 11 ( ( PUNCT bjmsr-311 157 12 22 22 NUM bjmsr-311 157 13 ) ) PUNCT bjmsr-311 157 14 for for ADP bjmsr-311 157 15 1 1 NOUN bjmsr-311 157 16 . . PUNCT bjmsr-311 158 1 that that PRON bjmsr-311 158 2 is be AUX bjmsr-311 158 3 , , PUNCT bjmsr-311 158 4 1 1 NOUN bjmsr-311 159 1 = = PUNCT bjmsr-311 159 2 yp yp X bjmsr-311 160 1 2x2p 2x2p NOUN bjmsr-311 160 2 = = PUNCT bjmsr-311 160 3 yq yq PROPN bjmsr-311 160 4 2x2q 2x2q PROPN bjmsr-311 160 5 ( ( PUNCT bjmsr-311 160 6 27 27 NUM bjmsr-311 160 7 ) ) PUNCT bjmsr-311 160 8 the the DET bjmsr-311 160 9 equality equality NOUN bjmsr-311 160 10 of of ADP bjmsr-311 160 11 sq sq PROPN bjmsr-311 160 12 and and CCONJ bjmsr-311 160 13 sp sp NOUN bjmsr-311 160 14 is be AUX bjmsr-311 160 15 because because SCONJ bjmsr-311 160 16 the the DET bjmsr-311 160 17 points point NOUN bjmsr-311 160 18 p p NOUN bjmsr-311 160 19 and and CCONJ bjmsr-311 160 20 q q NOUN bjmsr-311 160 21 are be AUX bjmsr-311 160 22 on on ADP bjmsr-311 160 23 the the DET bjmsr-311 160 24 regression regression NOUN bjmsr-311 160 25 line line NOUN bjmsr-311 160 26 and and CCONJ bjmsr-311 160 27 therefore therefore ADV bjmsr-311 160 28 up up ADP bjmsr-311 160 29 = = PROPN bjmsr-311 160 30 uq=0 uq=0 NOUN bjmsr-311 160 31 . . PUNCT bjmsr-311 161 1 thus thus ADV bjmsr-311 161 2 , , PUNCT bjmsr-311 161 3 sp sp PROPN bjmsr-311 161 4 = = SYM bjmsr-311 161 5 sq sq NOUN bjmsr-311 161 6 , , PUNCT bjmsr-311 161 7 so so ADV bjmsr-311 161 8 , , PUNCT bjmsr-311 161 9 the the DET bjmsr-311 161 10 values value NOUN bjmsr-311 161 11 of of ADP bjmsr-311 161 12 2 2 NOUN bjmsr-311 161 13 p p NOUN bjmsr-311 161 14 and and CCONJ bjmsr-311 161 15 2 2 NOUN bjmsr-311 161 16 q q NOUN bjmsr-311 161 17 derived derive VERB bjmsr-311 161 18 by by ADP bjmsr-311 161 19 minimizing minimize VERB bjmsr-311 161 20 either either PRON bjmsr-311 161 21 sp sp ADP bjmsr-311 161 22 or or CCONJ bjmsr-311 161 23 sq sq PROPN bjmsr-311 161 24 must must AUX bjmsr-311 161 25 be be AUX bjmsr-311 161 26 equal equal ADJ bjmsr-311 161 27 . . PUNCT bjmsr-311 162 1 this this PRON bjmsr-311 162 2 gives give VERB bjmsr-311 162 3 a a DET bjmsr-311 162 4 criterion criterion NOUN bjmsr-311 162 5 to to PART bjmsr-311 162 6 find find VERB bjmsr-311 162 7 the the DET bjmsr-311 162 8 desired desire VERB bjmsr-311 162 9 2 2 NOUN bjmsr-311 162 10 from from ADP bjmsr-311 162 11 all all DET bjmsr-311 162 12 2 2 ADJ bjmsr-311 162 13 k1 k1 NOUN bjmsr-311 162 14 for for ADP bjmsr-311 162 15 k1=1, k1=1, NOUN bjmsr-311 162 16 ... ... PUNCT bjmsr-311 162 17 ,n ,n NOUN bjmsr-311 162 18 . . PUNCT bjmsr-311 163 1 that that PRON bjmsr-311 163 2 is be AUX bjmsr-311 163 3 , , PUNCT bjmsr-311 163 4 when when SCONJ bjmsr-311 163 5 2 2 PROPN bjmsr-311 163 6 p=2 p=2 PROPN bjmsr-311 163 7 q. q. PROPN bjmsr-311 163 8 the the DET bjmsr-311 163 9 estimated estimate VERB bjmsr-311 163 10 value value NOUN bjmsr-311 163 11 of of ADP bjmsr-311 163 12 2 2 NOUN bjmsr-311 163 13 is be AUX bjmsr-311 163 14 denoted denote VERB bjmsr-311 163 15 by by ADP bjmsr-311 163 16 2^. 2^. DET bjmsr-311 163 17 value value NOUN bjmsr-311 163 18 of of ADP bjmsr-311 163 19 1^ 1^ ADJ bjmsr-311 163 20 is be AUX bjmsr-311 163 21 simply simply ADV bjmsr-311 163 22 computed compute VERB bjmsr-311 163 23 by by ADP bjmsr-311 163 24 ( ( PUNCT bjmsr-311 163 25 27 27 NUM bjmsr-311 163 26 ) ) PUNCT bjmsr-311 163 27 . . PUNCT bjmsr-311 164 1 now now ADV bjmsr-311 164 2 let let VERB bjmsr-311 164 3 us we PRON bjmsr-311 164 4 summarize summarize VERB bjmsr-311 164 5 the the DET bjmsr-311 164 6 whole whole ADJ bjmsr-311 164 7 procedure procedure NOUN bjmsr-311 164 8 for for ADP bjmsr-311 164 9 finding find VERB bjmsr-311 164 10 the the DET bjmsr-311 164 11 values value NOUN bjmsr-311 164 12 of of ADP bjmsr-311 164 13 1^ 1^ ADJ bjmsr-311 164 14 and and CCONJ bjmsr-311 164 15 2^ 2^ VERB bjmsr-311 164 16 for for ADP bjmsr-311 164 17 the the DET bjmsr-311 164 18 model model NOUN bjmsr-311 164 19 given give VERB bjmsr-311 164 20 by by ADP bjmsr-311 164 21 ( ( PUNCT bjmsr-311 164 22 16 16 NUM bjmsr-311 164 23 ) ) PUNCT bjmsr-311 164 24 . . PUNCT bjmsr-311 165 1 crude crude ADJ bjmsr-311 165 2 algorithm algorithm NOUN bjmsr-311 165 3 1 1 NUM bjmsr-311 165 4 step step NOUN bjmsr-311 165 5 0 0 NUM bjmsr-311 165 6 ) ) PUNCT bjmsr-311 165 7 set set VERB bjmsr-311 165 8 k1=1 k1=1 PROPN bjmsr-311 165 9 . . PUNCT bjmsr-311 166 1 step step NOUN bjmsr-311 166 2 1 1 NUM bjmsr-311 166 3 ) ) PUNCT bjmsr-311 166 4 compute compute NOUN bjmsr-311 166 5 ( ( PUNCT bjmsr-311 166 6 18 18 NUM bjmsr-311 166 7 ) ) PUNCT bjmsr-311 166 8 . . PUNCT bjmsr-311 167 1 step step NOUN bjmsr-311 167 2 2 2 NUM bjmsr-311 167 3 ) ) PUNCT bjmsr-311 167 4 minimize minimize NOUN bjmsr-311 167 5 ( ( PUNCT bjmsr-311 167 6 21 21 NUM bjmsr-311 167 7 ) ) PUNCT bjmsr-311 167 8 by by ADP bjmsr-311 167 9 using use VERB bjmsr-311 167 10 the the DET bjmsr-311 167 11 weighted weight VERB bjmsr-311 167 12 median median ADJ bjmsr-311 167 13 procedure procedure NOUN bjmsr-311 167 14 and and CCONJ bjmsr-311 167 15 find find VERB bjmsr-311 167 16 ß2 ß2 NOUN bjmsr-311 167 17 k1 k1 NOUN bjmsr-311 167 18 . . PUNCT bjmsr-311 168 1 step step NOUN bjmsr-311 168 2 3 3 NUM bjmsr-311 168 3 ) ) PUNCT bjmsr-311 168 4 check check NOUN bjmsr-311 168 5 if if SCONJ bjmsr-311 168 6 ß2 ß2 NOUN bjmsr-311 168 7 k1 k1 NOUN bjmsr-311 168 8 = = SYM bjmsr-311 168 9 ß2 ß2 NOUN bjmsr-311 168 10 k1 k1 PROPN bjmsr-311 168 11 - - PUNCT bjmsr-311 168 12 k k NOUN bjmsr-311 168 13 for for ADP bjmsr-311 168 14 0 0 NUM bjmsr-311 168 15 < < X bjmsr-311 168 16 k k X bjmsr-311 168 17 < < X bjmsr-311 168 18 k1 k1 X bjmsr-311 168 19 , , PUNCT bjmsr-311 168 20 then then ADV bjmsr-311 168 21 set set VERB bjmsr-311 168 22 ß2^=ß2 ß2^=ß2 PRON bjmsr-311 168 23 k1 k1 NOUN bjmsr-311 168 24 and and CCONJ bjmsr-311 168 25 ß1^=yk1 ß1^=yk1 NOUN bjmsr-311 168 26 - - PUNCT bjmsr-311 168 27 ß2^x2k1 ß2^x2k1 NOUN bjmsr-311 168 28 then then ADV bjmsr-311 168 29 stop stop NOUN bjmsr-311 168 30 . . PUNCT bjmsr-311 169 1 step step NOUN bjmsr-311 169 2 4 4 NUM bjmsr-311 169 3 ) ) PUNCT bjmsr-311 169 4 increase increase NOUN bjmsr-311 169 5 k1 k1 NOUN bjmsr-311 169 6 by by ADP bjmsr-311 169 7 one one NUM bjmsr-311 169 8 and and CCONJ bjmsr-311 169 9 go go VERB bjmsr-311 169 10 to to PART bjmsr-311 169 11 step step VERB bjmsr-311 169 12 1 1 NUM bjmsr-311 169 13 . . NOUN bjmsr-311 169 14 3.2 3.2 NUM bjmsr-311 169 15 algorithm algorithm NOUN bjmsr-311 169 16 2 2 NUM bjmsr-311 169 17 the the DET bjmsr-311 169 18 crude crude ADJ bjmsr-311 169 19 algorithm algorithm NOUN bjmsr-311 169 20 1 1 NUM bjmsr-311 169 21 for for ADP bjmsr-311 169 22 finding find VERB bjmsr-311 169 23 ß1^ ß1^ NOUN bjmsr-311 169 24 and and CCONJ bjmsr-311 169 25 ß2^ ß2^ NOUN bjmsr-311 169 26 is be AUX bjmsr-311 169 27 not not PART bjmsr-311 169 28 computationally computationally ADV bjmsr-311 169 29 efficient efficient ADJ bjmsr-311 169 30 because because SCONJ bjmsr-311 169 31 it it PRON bjmsr-311 169 32 usually usually ADV bjmsr-311 169 33 requires require VERB bjmsr-311 169 34 testing test VERB bjmsr-311 169 35 the the DET bjmsr-311 169 36 majority majority NOUN bjmsr-311 169 37 of of ADP bjmsr-311 169 38 observations observation NOUN bjmsr-311 169 39 . . PUNCT bjmsr-311 170 1 in in ADP bjmsr-311 170 2 order order NOUN bjmsr-311 170 3 to to PART bjmsr-311 170 4 make make VERB bjmsr-311 170 5 this this DET bjmsr-311 170 6 algorithm algorithm NOUN bjmsr-311 170 7 efficient efficient ADJ bjmsr-311 170 8 , , PUNCT bjmsr-311 170 9 some some DET bjmsr-311 170 10 elaborations elaboration NOUN bjmsr-311 170 11 are be AUX bjmsr-311 170 12 necessary necessary ADJ bjmsr-311 170 13 . . PUNCT bjmsr-311 171 1 instead instead ADV bjmsr-311 171 2 of of ADP bjmsr-311 171 3 setting set VERB bjmsr-311 171 4 k1=1 k1=1 PROPN bjmsr-311 171 5 , , PUNCT bjmsr-311 171 6 let let VERB bjmsr-311 171 7 us we PRON bjmsr-311 171 8 set set VERB bjmsr-311 171 9 k1 k1 NOUN bjmsr-311 171 10 equal equal ADJ bjmsr-311 171 11 to to ADP bjmsr-311 171 12 an an DET bjmsr-311 171 13 arbitrary arbitrary ADJ bjmsr-311 171 14 integer integer NOUN bjmsr-311 171 15 value value NOUN bjmsr-311 171 16 such such ADJ bjmsr-311 171 17 as as ADP bjmsr-311 171 18 a a DET bjmsr-311 171 19 where where SCONJ bjmsr-311 171 20 a a PRON bjmsr-311 171 21 is be AUX bjmsr-311 171 22 any any DET bjmsr-311 171 23 integer integer NOUN bjmsr-311 171 24 from from ADP bjmsr-311 171 25 one one NUM bjmsr-311 171 26 to to ADP bjmsr-311 171 27 n. n. PROPN bjmsr-311 171 28 suppose suppose VERB bjmsr-311 171 29 now now ADV bjmsr-311 171 30 , , PUNCT bjmsr-311 171 31 ua ua PROPN bjmsr-311 171 32 = = PROPN bjmsr-311 171 33 ya ya NOUN bjmsr-311 171 34 - - PUNCT bjmsr-311 171 35 ß1 ß1 PROPN bjmsr-311 171 36 - - PUNCT bjmsr-311 171 37 ß2x2a=0 ß2x2a=0 PROPN bjmsr-311 171 38 , , PUNCT bjmsr-311 171 39 and and CCONJ bjmsr-311 171 40 rewrite rewrite VERB bjmsr-311 171 41 ( ( PUNCT bjmsr-311 171 42 21 21 NUM bjmsr-311 171 43 ) ) PUNCT bjmsr-311 171 44 as as ADP bjmsr-311 171 45 , , PUNCT bjmsr-311 171 46 n n PRON bjmsr-311 171 47 min min NOUN bjmsr-311 171 48 : : PUNCT bjmsr-311 171 49 sa sa PROPN bjmsr-311 171 50 = = PROPN bjmsr-311 171 51 σ σ PROPN bjmsr-311 171 52 │ │ NOUN bjmsr-311 171 53 yi yi NOUN bjmsr-311 171 54 a a DET bjmsr-311 171 55 ß2x2i ß2x2i NUM bjmsr-311 171 56 a a DET bjmsr-311 171 57 │ │ X bjmsr-311 171 58 ( ( PUNCT bjmsr-311 171 59 28 28 NUM bjmsr-311 171 60 ) ) PUNCT bjmsr-311 171 61 ß2 ß2 NOUN bjmsr-311 171 62 i=1 i=1 PRON bjmsr-311 171 63 minimizing minimize VERB bjmsr-311 171 64 ( ( PUNCT bjmsr-311 171 65 28 28 NUM bjmsr-311 171 66 ) ) PUNCT bjmsr-311 171 67 gives give VERB bjmsr-311 171 68 ß2 ß2 PROPN bjmsr-311 171 69 a a PRON bjmsr-311 171 70 which which PRON bjmsr-311 171 71 is be AUX bjmsr-311 171 72 equal equal ADJ bjmsr-311 171 73 to to ADP bjmsr-311 171 74 yb yb PROPN bjmsr-311 171 75 a a DET bjmsr-311 171 76 yb yb PROPN bjmsr-311 172 1 ya ya PROPN bjmsr-311 172 2 ß2 ß2 VERB bjmsr-311 172 3 a a DET bjmsr-311 172 4 = = PUNCT bjmsr-311 172 5 ─ ─ ADJ bjmsr-311 172 6 ─ ─ X bjmsr-311 172 7 ─ ─ PROPN bjmsr-311 172 8 = = PUNCT bjmsr-311 173 1 ─ ─ PUNCT bjmsr-311 173 2 ─ ─ ADJ bjmsr-311 173 3 ─ ─ ADJ bjmsr-311 173 4 ─ ─ ADJ bjmsr-311 173 5 ─ ─ X bjmsr-311 173 6 ( ( PUNCT bjmsr-311 173 7 29 29 NUM bjmsr-311 173 8 ) ) PUNCT bjmsr-311 173 9 x2b x2b NOUN bjmsr-311 174 1 a a PRON bjmsr-311 174 2 x2b x2b NUM bjmsr-311 175 1 x2a x2a PROPN bjmsr-311 175 2 copyright copyright PROPN bjmsr-311 175 3 © © PROPN bjmsr-311 175 4 cc cc PROPN bjmsr-311 175 5 - - PUNCT bjmsr-311 175 6 by by ADP bjmsr-311 175 7 - - PUNCT bjmsr-311 175 8 nc nc PROPN bjmsr-311 175 9 2019 2019 NUM bjmsr-311 175 10 , , PUNCT bjmsr-311 175 11 bjmsr bjmsr PROPN bjmsr-311 175 12 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 175 13 bangladesh bangladesh PROPN bjmsr-311 175 14 journal journal PROPN bjmsr-311 175 15 of of ADP bjmsr-311 175 16 multidisciplinary multidisciplinary ADJ bjmsr-311 175 17 scientific scientific ADJ bjmsr-311 175 18 research research NOUN bjmsr-311 175 19 vol vol NOUN bjmsr-311 175 20 . . PROPN bjmsr-311 175 21 1 1 NUM bjmsr-311 175 22 , , PUNCT bjmsr-311 175 23 no no INTJ bjmsr-311 175 24 . . NOUN bjmsr-311 175 25 1 1 NUM bjmsr-311 175 26 ; ; PUNCT bjmsr-311 175 27 2019 2019 NUM bjmsr-311 175 28 7 7 NUM bjmsr-311 175 29 on on ADP bjmsr-311 175 30 the the DET bjmsr-311 175 31 other other ADJ bjmsr-311 175 32 hand hand NOUN bjmsr-311 175 33 , , PUNCT bjmsr-311 175 34 by by ADP bjmsr-311 175 35 pivoting pivot VERB bjmsr-311 175 36 on on ADP bjmsr-311 175 37 the the DET bjmsr-311 175 38 ath ath NOUN bjmsr-311 175 39 observation observation NOUN bjmsr-311 175 40 , , PUNCT bjmsr-311 175 41 another another DET bjmsr-311 175 42 point point NOUN bjmsr-311 175 43 such such ADJ bjmsr-311 175 44 as as ADP bjmsr-311 175 45 b b PROPN bjmsr-311 175 46 is be AUX bjmsr-311 175 47 found find VERB bjmsr-311 175 48 where where SCONJ bjmsr-311 175 49 b b NOUN bjmsr-311 175 50 refers refer VERB bjmsr-311 175 51 to to ADP bjmsr-311 175 52 that that DET bjmsr-311 175 53 observation observation NOUN bjmsr-311 175 54 which which PRON bjmsr-311 175 55 has have VERB bjmsr-311 175 56 zero zero NUM bjmsr-311 175 57 error error NOUN bjmsr-311 175 58 in in ADP bjmsr-311 175 59 the the DET bjmsr-311 175 60 minimum minimum ADJ bjmsr-311 175 61 solution solution NOUN bjmsr-311 175 62 of of ADP bjmsr-311 175 63 ( ( PUNCT bjmsr-311 175 64 28 28 NUM bjmsr-311 175 65 ) ) PUNCT bjmsr-311 175 66 , , PUNCT bjmsr-311 175 67 so so ADV bjmsr-311 175 68 , , PUNCT bjmsr-311 175 69 ub ub PROPN bjmsr-311 175 70 = = PROPN bjmsr-311 175 71 yb yb ADJ bjmsr-311 175 72 - - PUNCT bjmsr-311 175 73 ß1 ß1 NOUN bjmsr-311 175 74 - - PUNCT bjmsr-311 175 75 ß2x2b=0 ß2x2b=0 PROPN bjmsr-311 175 76 . . PUNCT bjmsr-311 176 1 let let VERB bjmsr-311 176 2 us we PRON bjmsr-311 176 3 denote denote VERB bjmsr-311 176 4 the the DET bjmsr-311 176 5 minimum minimum NOUN bjmsr-311 176 6 of of ADP bjmsr-311 176 7 sa sa NOUN bjmsr-311 176 8 in in ADP bjmsr-311 176 9 ( ( PUNCT bjmsr-311 176 10 28 28 NUM bjmsr-311 176 11 ) ) PUNCT bjmsr-311 176 12 as as ADP bjmsr-311 176 13 sa sa PROPN bjmsr-311 176 14 * * PROPN bjmsr-311 176 15 , , PUNCT bjmsr-311 176 16 then then ADV bjmsr-311 176 17 , , PUNCT bjmsr-311 176 18 n n PRON bjmsr-311 176 19 sa sa NOUN bjmsr-311 176 20 * * PUNCT bjmsr-311 177 1 = = PUNCT bjmsr-311 177 2 σ σ PROPN bjmsr-311 177 3 │ │ NOUN bjmsr-311 177 4 yi yi NOUN bjmsr-311 177 5 a a DET bjmsr-311 177 6 ß2 ß2 NOUN bjmsr-311 177 7 ax2i ax2i PROPN bjmsr-311 177 8 a a PRON bjmsr-311 177 9 │ │ X bjmsr-311 177 10 ( ( PUNCT bjmsr-311 177 11 30 30 NUM bjmsr-311 177 12 ) ) PUNCT bjmsr-311 177 13 i=1 i=1 PRON bjmsr-311 177 14 note note VERB bjmsr-311 177 15 that that SCONJ bjmsr-311 177 16 , , PUNCT bjmsr-311 177 17 ß1 ß1 PROPN bjmsr-311 177 18 = = SYM bjmsr-311 177 19 ya ya PROPN bjmsr-311 177 20 ß2 ß2 VERB bjmsr-311 177 21 ax2 ax2 NOUN bjmsr-311 177 22 a a DET bjmsr-311 177 23 = = SYM bjmsr-311 177 24 yb yb PROPN bjmsr-311 177 25 ß2 ß2 PROPN bjmsr-311 177 26 ax2b ax2b PROPN bjmsr-311 177 27 ( ( PUNCT bjmsr-311 177 28 31 31 NUM bjmsr-311 177 29 ) ) PUNCT bjmsr-311 177 30 this this PRON bjmsr-311 177 31 comes come VERB bjmsr-311 177 32 from from ADP bjmsr-311 177 33 multiplying multiply VERB bjmsr-311 177 34 ( ( PUNCT bjmsr-311 177 35 29 29 NUM bjmsr-311 177 36 ) ) PUNCT bjmsr-311 177 37 by by ADP bjmsr-311 177 38 its its PRON bjmsr-311 177 39 denominator denominator NOUN bjmsr-311 177 40 and and CCONJ bjmsr-311 177 41 rearranging rearrange VERB bjmsr-311 177 42 the the DET bjmsr-311 177 43 terms term NOUN bjmsr-311 177 44 . . PUNCT bjmsr-311 178 1 substitute substitute NOUN bjmsr-311 178 2 ( ( PUNCT bjmsr-311 178 3 31 31 NUM bjmsr-311 178 4 ) ) PUNCT bjmsr-311 178 5 in in ADP bjmsr-311 178 6 ( ( PUNCT bjmsr-311 178 7 17 17 NUM bjmsr-311 178 8 ) ) PUNCT bjmsr-311 178 9 , , PUNCT bjmsr-311 178 10 n n CCONJ bjmsr-311 178 11 n n PROPN bjmsr-311 178 12 s s NOUN bjmsr-311 178 13 = = SYM bjmsr-311 178 14 σ σ PROPN bjmsr-311 178 15 │ │ NOUN bjmsr-311 178 16 yi yi PROPN bjmsr-311 178 17 - - PUNCT bjmsr-311 178 18 ya ya NOUN bjmsr-311 178 19 - - PUNCT bjmsr-311 178 20 ß2 ß2 NOUN bjmsr-311 178 21 a(x2i a(x2i NOUN bjmsr-311 178 22 - - PUNCT bjmsr-311 178 23 x2 x2 PROPN bjmsr-311 178 24 a a NOUN bjmsr-311 178 25 ) ) PUNCT bjmsr-311 178 26 │ │ NOUN bjmsr-311 178 27 = = SYM bjmsr-311 178 28 σ σ PROPN bjmsr-311 178 29 │ │ NOUN bjmsr-311 178 30 yi yi PROPN bjmsr-311 178 31 - - PUNCT bjmsr-311 178 32 yb yb PROPN bjmsr-311 178 33 - - PUNCT bjmsr-311 178 34 ß2 ß2 NOUN bjmsr-311 178 35 a(x2i a(x2i NOUN bjmsr-311 178 36 - - PUNCT bjmsr-311 178 37 x2a x2a PROPN bjmsr-311 178 38 ) ) PUNCT bjmsr-311 178 39 │ │ X bjmsr-311 178 40 i=1 i=1 PROPN bjmsr-311 178 41 i=1 i=1 X bjmsr-311 178 42 or or CCONJ bjmsr-311 178 43 , , PUNCT bjmsr-311 178 44 n n CCONJ bjmsr-311 178 45 n n PROPN bjmsr-311 178 46 s s NOUN bjmsr-311 178 47 = = SYM bjmsr-311 178 48 σ σ PROPN bjmsr-311 178 49 │ │ NOUN bjmsr-311 178 50 yi yi PROPN bjmsr-311 178 51 a a DET bjmsr-311 178 52 - - PUNCT bjmsr-311 178 53 ß2 ß2 NOUN bjmsr-311 178 54 ax2i ax2i PROPN bjmsr-311 178 55 a a DET bjmsr-311 178 56 │ │ NOUN bjmsr-311 178 57 = = SYM bjmsr-311 178 58 σ σ PROPN bjmsr-311 178 59 │ │ NOUN bjmsr-311 178 60 yi yi PROPN bjmsr-311 178 61 b b NOUN bjmsr-311 178 62 - - PUNCT bjmsr-311 178 63 ß2 ß2 VERB bjmsr-311 178 64 ax2i ax2i PROPN bjmsr-311 178 65 b b PROPN bjmsr-311 178 66 │ │ X bjmsr-311 178 67 ( ( PUNCT bjmsr-311 178 68 32 32 NUM bjmsr-311 178 69 ) ) PUNCT bjmsr-311 178 70 i=1 i=1 VERB bjmsr-311 179 1 i=1 i=1 PROPN bjmsr-311 179 2 using use VERB bjmsr-311 179 3 ( ( PUNCT bjmsr-311 179 4 30 30 NUM bjmsr-311 179 5 ) ) PUNCT bjmsr-311 179 6 the the DET bjmsr-311 179 7 first first ADJ bjmsr-311 179 8 sum sum NOUN bjmsr-311 179 9 in in ADP bjmsr-311 179 10 ( ( PUNCT bjmsr-311 179 11 32 32 NUM bjmsr-311 179 12 ) ) PUNCT bjmsr-311 179 13 is be AUX bjmsr-311 179 14 sa sa NOUN bjmsr-311 179 15 * * PUNCT bjmsr-311 179 16 and and CCONJ bjmsr-311 179 17 the the DET bjmsr-311 179 18 second second ADJ bjmsr-311 179 19 sum sum NOUN bjmsr-311 179 20 is be AUX bjmsr-311 179 21 sb sb PROPN bjmsr-311 179 22 evaluated evaluate VERB bjmsr-311 179 23 at at ADP bjmsr-311 179 24 ß2 ß2 NOUN bjmsr-311 179 25 = = SYM bjmsr-311 179 26 ß2 ß2 NOUN bjmsr-311 179 27 a. a. NOUN bjmsr-311 179 28 thus thus ADV bjmsr-311 179 29 , , PUNCT bjmsr-311 179 30 it it PRON bjmsr-311 179 31 can can AUX bjmsr-311 179 32 be be AUX bjmsr-311 179 33 concluded conclude VERB bjmsr-311 179 34 that that SCONJ bjmsr-311 179 35 , , PUNCT bjmsr-311 179 36 sa sa PROPN bjmsr-311 179 37 * * PUNCT bjmsr-311 179 38 = = PUNCT bjmsr-311 179 39 sb sb PROPN bjmsr-311 179 40 │ │ X bjmsr-311 179 41 ( ( PUNCT bjmsr-311 179 42 33 33 NUM bjmsr-311 179 43 ) ) PUNCT bjmsr-311 179 44 │ │ NOUN bjmsr-311 179 45 ß2 ß2 NOUN bjmsr-311 179 46 = = SYM bjmsr-311 179 47 ß2 ß2 NOUN bjmsr-311 179 48 a a DET bjmsr-311 179 49 sa sa NOUN bjmsr-311 179 50 * * PUNCT bjmsr-311 179 51 is be AUX bjmsr-311 179 52 at at ADP bjmsr-311 179 53 the the DET bjmsr-311 179 54 minimum minimum NOUN bjmsr-311 179 55 but but CCONJ bjmsr-311 179 56 sb sb NOUN bjmsr-311 179 57 │ │ PROPN bjmsr-311 179 58 still still ADV bjmsr-311 179 59 can can AUX bjmsr-311 179 60 be be AUX bjmsr-311 179 61 minimized minimize VERB bjmsr-311 179 62 for for ADP bjmsr-311 179 63 other other ADJ bjmsr-311 179 64 values value NOUN bjmsr-311 179 65 of of ADP bjmsr-311 179 66 ß2 ß2 NOUN bjmsr-311 179 67 . . PUNCT bjmsr-311 180 1 │ │ VERB bjmsr-311 180 2 ß2 ß2 NOUN bjmsr-311 180 3 = = SYM bjmsr-311 180 4 ß2 ß2 NOUN bjmsr-311 180 5 a a PRON bjmsr-311 180 6 therefore therefore ADV bjmsr-311 180 7 , , PUNCT bjmsr-311 180 8 an an DET bjmsr-311 180 9 important important ADJ bjmsr-311 180 10 result result NOUN bjmsr-311 180 11 is be AUX bjmsr-311 180 12 derived derive VERB bjmsr-311 180 13 , , PUNCT bjmsr-311 180 14 that that ADV bjmsr-311 180 15 is is ADV bjmsr-311 180 16 , , PUNCT bjmsr-311 180 17 sa sa PROPN bjmsr-311 180 18 * * PUNCT bjmsr-311 180 19 > > X bjmsr-311 180 20 sb sb PROPN bjmsr-311 181 1 * * PROPN bjmsr-311 181 2 ( ( PUNCT bjmsr-311 181 3 34 34 NUM bjmsr-311 181 4 ) ) PUNCT bjmsr-311 181 5 the the DET bjmsr-311 181 6 inequality inequality NOUN bjmsr-311 181 7 of of ADP bjmsr-311 181 8 ( ( PUNCT bjmsr-311 181 9 34 34 NUM bjmsr-311 181 10 ) ) PUNCT bjmsr-311 181 11 guarantees guarantee VERB bjmsr-311 181 12 that that SCONJ bjmsr-311 181 13 if if SCONJ bjmsr-311 181 14 we we PRON bjmsr-311 181 15 choose choose VERB bjmsr-311 181 16 an an DET bjmsr-311 181 17 arbitrary arbitrary ADJ bjmsr-311 181 18 point point NOUN bjmsr-311 181 19 to to PART bjmsr-311 181 20 transfer transfer VERB bjmsr-311 181 21 the the DET bjmsr-311 181 22 origin origin NOUN bjmsr-311 181 23 of of ADP bjmsr-311 181 24 coordinates coordinate NOUN bjmsr-311 181 25 to to ADP bjmsr-311 181 26 it it PRON bjmsr-311 181 27 and and CCONJ bjmsr-311 181 28 minimizing minimize VERB bjmsr-311 181 29 the the DET bjmsr-311 181 30 objective objective ADJ bjmsr-311 181 31 function function NOUN bjmsr-311 181 32 ( ( PUNCT bjmsr-311 181 33 21 21 NUM bjmsr-311 181 34 ) ) PUNCT bjmsr-311 181 35 another another DET bjmsr-311 181 36 point point NOUN bjmsr-311 181 37 is be AUX bjmsr-311 181 38 found find VERB bjmsr-311 181 39 , , PUNCT bjmsr-311 181 40 then then ADV bjmsr-311 181 41 transferring transfer VERB bjmsr-311 181 42 the the DET bjmsr-311 181 43 origin origin NOUN bjmsr-311 181 44 to to ADP bjmsr-311 181 45 this this DET bjmsr-311 181 46 newly newly ADV bjmsr-311 181 47 found find VERB bjmsr-311 181 48 point point NOUN bjmsr-311 181 49 decreases decrease VERB bjmsr-311 181 50 the the DET bjmsr-311 181 51 total total ADJ bjmsr-311 181 52 sum sum NOUN bjmsr-311 181 53 of of ADP bjmsr-311 181 54 absolute absolute ADJ bjmsr-311 181 55 errors error NOUN bjmsr-311 181 56 . . PUNCT bjmsr-311 182 1 therefore therefore ADV bjmsr-311 182 2 , , PUNCT bjmsr-311 182 3 at at ADP bjmsr-311 182 4 each each DET bjmsr-311 182 5 transference transference NOUN bjmsr-311 182 6 we we PRON bjmsr-311 182 7 get get VERB bjmsr-311 182 8 closer close ADJ bjmsr-311 182 9 to to ADP bjmsr-311 182 10 the the DET bjmsr-311 182 11 minimum minimum NOUN bjmsr-311 182 12 of of ADP bjmsr-311 182 13 s. s. PROPN bjmsr-311 182 14 by by ADP bjmsr-311 182 15 a a DET bjmsr-311 182 16 similar similar ADJ bjmsr-311 182 17 discussion discussion NOUN bjmsr-311 182 18 , , PUNCT bjmsr-311 182 19 this this DET bjmsr-311 182 20 conclusion conclusion NOUN bjmsr-311 182 21 can can AUX bjmsr-311 182 22 be be AUX bjmsr-311 182 23 generalized generalize VERB bjmsr-311 182 24 as as ADP bjmsr-311 182 25 , , PUNCT bjmsr-311 182 26 sa sa PROPN bjmsr-311 182 27 * * PUNCT bjmsr-311 182 28 > > X bjmsr-311 182 29 sb sb PROPN bjmsr-311 182 30 * * PROPN bjmsr-311 182 31 > > X bjmsr-311 182 32 sc sc PROPN bjmsr-311 182 33 * * PUNCT bjmsr-311 182 34 > > X bjmsr-311 182 35 sd sd PROPN bjmsr-311 182 36 * * PUNCT bjmsr-311 182 37 ... ... PUNCT bjmsr-311 183 1 ( ( PUNCT bjmsr-311 183 2 35 35 NUM bjmsr-311 183 3 ) ) PUNCT bjmsr-311 183 4 note note NOUN bjmsr-311 183 5 that that SCONJ bjmsr-311 183 6 a a PRON bjmsr-311 183 7 is be AUX bjmsr-311 183 8 an an DET bjmsr-311 183 9 arbitrary arbitrary ADJ bjmsr-311 183 10 starting starting NOUN bjmsr-311 183 11 point point NOUN bjmsr-311 183 12 . . PUNCT bjmsr-311 184 1 the the DET bjmsr-311 184 2 point point NOUN bjmsr-311 184 3 b b NOUN bjmsr-311 184 4 is be AUX bjmsr-311 184 5 derived derive VERB bjmsr-311 184 6 by by ADP bjmsr-311 184 7 minimizing minimize VERB bjmsr-311 184 8 sa sa PROPN bjmsr-311 184 9 , , PUNCT bjmsr-311 184 10 c c PROPN bjmsr-311 184 11 is be AUX bjmsr-311 184 12 derived derive VERB bjmsr-311 184 13 by by ADP bjmsr-311 184 14 minimizing minimize VERB bjmsr-311 184 15 sb sb PROPN bjmsr-311 184 16 , , PUNCT bjmsr-311 184 17 and and CCONJ bjmsr-311 184 18 d d NOUN bjmsr-311 184 19 is be AUX bjmsr-311 184 20 derived derive VERB bjmsr-311 184 21 by by ADP bjmsr-311 184 22 minimizing minimize VERB bjmsr-311 184 23 sc sc PROPN bjmsr-311 184 24 , , PUNCT bjmsr-311 184 25 and and CCONJ bjmsr-311 184 26 so so ADV bjmsr-311 184 27 on on ADV bjmsr-311 184 28 . . PUNCT bjmsr-311 185 1 now now ADV bjmsr-311 185 2 , , PUNCT bjmsr-311 185 3 the the DET bjmsr-311 185 4 question question NOUN bjmsr-311 185 5 is be AUX bjmsr-311 185 6 , , PUNCT bjmsr-311 185 7 when when SCONJ bjmsr-311 185 8 the the DET bjmsr-311 185 9 minimum minimum ADJ bjmsr-311 185 10 value value NOUN bjmsr-311 185 11 of of ADP bjmsr-311 185 12 s s PRON bjmsr-311 185 13 is be AUX bjmsr-311 185 14 reached reach VERB bjmsr-311 185 15 ? ? PUNCT bjmsr-311 186 1 suppose suppose VERB bjmsr-311 186 2 s*=sf s*=sf NOUN bjmsr-311 186 3 * * PUNCT bjmsr-311 186 4 ; ; PUNCT bjmsr-311 186 5 by by ADP bjmsr-311 186 6 transferring transfer VERB bjmsr-311 186 7 the the DET bjmsr-311 186 8 origin origin NOUN bjmsr-311 186 9 of of ADP bjmsr-311 186 10 coordinates coordinate NOUN bjmsr-311 186 11 to to ADP bjmsr-311 186 12 the the DET bjmsr-311 186 13 point point NOUN bjmsr-311 186 14 f f PROPN bjmsr-311 186 15 and and CCONJ bjmsr-311 186 16 minimizing minimize VERB bjmsr-311 186 17 sf sf PROPN bjmsr-311 186 18 , , PUNCT bjmsr-311 186 19 the the DET bjmsr-311 186 20 gth gth PROPN bjmsr-311 186 21 observation observation NOUN bjmsr-311 186 22 is be AUX bjmsr-311 186 23 derived derive VERB bjmsr-311 186 24 . . PUNCT bjmsr-311 187 1 when when SCONJ bjmsr-311 187 2 s*=sf s*=sf NOUN bjmsr-311 187 3 * * AUX bjmsr-311 187 4 by by ADP bjmsr-311 187 5 minimizing minimize VERB bjmsr-311 187 6 sg sg PROPN bjmsr-311 187 7 , , PUNCT bjmsr-311 187 8 fth fth ADJ bjmsr-311 187 9 observation observation NOUN bjmsr-311 187 10 is be AUX bjmsr-311 187 11 again again ADV bjmsr-311 187 12 found find VERB bjmsr-311 187 13 , , PUNCT bjmsr-311 187 14 because because SCONJ bjmsr-311 187 15 sg*=sf*=s sg*=sf*=s PROPN bjmsr-311 187 16 * * PUNCT bjmsr-311 187 17 and and CCONJ bjmsr-311 187 18 the the DET bjmsr-311 187 19 gth gth PROPN bjmsr-311 187 20 and and CCONJ bjmsr-311 187 21 fth fth PROPN bjmsr-311 187 22 observations observation NOUN bjmsr-311 187 23 are be AUX bjmsr-311 187 24 both both PRON bjmsr-311 187 25 on on ADP bjmsr-311 187 26 the the DET bjmsr-311 187 27 l1 l1 PROPN bjmsr-311 187 28 norm norm PROPN bjmsr-311 187 29 regression regression NOUN bjmsr-311 187 30 line line NOUN bjmsr-311 187 31 . . PUNCT bjmsr-311 188 1 this this DET bjmsr-311 188 2 conclusion conclusion NOUN bjmsr-311 188 3 can can AUX bjmsr-311 188 4 be be AUX bjmsr-311 188 5 a a DET bjmsr-311 188 6 criterion criterion NOUN bjmsr-311 188 7 to to PART bjmsr-311 188 8 stop stop VERB bjmsr-311 188 9 the the DET bjmsr-311 188 10 procedure procedure NOUN bjmsr-311 188 11 . . PUNCT bjmsr-311 189 1 hence hence ADV bjmsr-311 189 2 , , PUNCT bjmsr-311 189 3 sa sa PROPN bjmsr-311 189 4 * * PUNCT bjmsr-311 189 5 > > X bjmsr-311 189 6 sb sb PROPN bjmsr-311 189 7 * * PROPN bjmsr-311 189 8 > > X bjmsr-311 189 9 sc sc PROPN bjmsr-311 189 10 * * PUNCT bjmsr-311 189 11 > > X bjmsr-311 189 12 sd sd PROPN bjmsr-311 189 13 * * PUNCT bjmsr-311 189 14 ... ... PUNCT bjmsr-311 190 1 > > X bjmsr-311 191 1 sf sf X bjmsr-311 191 2 * * PUNCT bjmsr-311 191 3 = = PUNCT bjmsr-311 191 4 sg sg PROPN bjmsr-311 191 5 * * PUNCT bjmsr-311 191 6 = = PUNCT bjmsr-311 191 7 s s X bjmsr-311 191 8 * * PUNCT bjmsr-311 191 9 ( ( PUNCT bjmsr-311 191 10 36 36 NUM bjmsr-311 191 11 ) ) PUNCT bjmsr-311 191 12 it it PRON bjmsr-311 191 13 should should AUX bjmsr-311 191 14 be be AUX bjmsr-311 191 15 noted note VERB bjmsr-311 191 16 that that SCONJ bjmsr-311 191 17 if if SCONJ bjmsr-311 191 18 the the DET bjmsr-311 191 19 minimum minimum ADJ bjmsr-311 191 20 solution solution NOUN bjmsr-311 191 21 of of ADP bjmsr-311 191 22 s s NOUN bjmsr-311 191 23 is be AUX bjmsr-311 191 24 not not PART bjmsr-311 191 25 unique unique ADJ bjmsr-311 191 26 , , PUNCT bjmsr-311 191 27 that that PRON bjmsr-311 191 28 is be AUX bjmsr-311 191 29 function function NOUN bjmsr-311 192 1 s s PART bjmsr-311 192 2 has have VERB bjmsr-311 192 3 a a DET bjmsr-311 192 4 horizontal horizontal ADJ bjmsr-311 192 5 segment segment NOUN bjmsr-311 192 6 , , PUNCT bjmsr-311 192 7 the the DET bjmsr-311 192 8 procedure procedure NOUN bjmsr-311 192 9 stops stop VERB bjmsr-311 192 10 when when SCONJ bjmsr-311 192 11 it it PRON bjmsr-311 192 12 reaches reach VERB bjmsr-311 192 13 the the DET bjmsr-311 192 14 first first ADJ bjmsr-311 192 15 minimum minimum ADJ bjmsr-311 192 16 solution solution NOUN bjmsr-311 192 17 . . PUNCT bjmsr-311 193 1 now now ADV bjmsr-311 193 2 , , PUNCT bjmsr-311 193 3 let let VERB bjmsr-311 193 4 us we PRON bjmsr-311 193 5 introduce introduce VERB bjmsr-311 193 6 the the DET bjmsr-311 193 7 whole whole ADJ bjmsr-311 193 8 stages stage NOUN bjmsr-311 193 9 of of ADP bjmsr-311 193 10 this this DET bjmsr-311 193 11 algorithm algorithm NOUN bjmsr-311 193 12 to to PART bjmsr-311 193 13 find find VERB bjmsr-311 193 14 the the DET bjmsr-311 193 15 l1 l1 PROPN bjmsr-311 193 16 norm norm NOUN bjmsr-311 193 17 estimates estimate NOUN bjmsr-311 193 18 of of ADP bjmsr-311 193 19 ß1 ß1 PROPN bjmsr-311 193 20 and and CCONJ bjmsr-311 193 21 ß2 ß2 NOUN bjmsr-311 193 22 in in ADP bjmsr-311 193 23 the the DET bjmsr-311 193 24 simple simple ADJ bjmsr-311 193 25 linear linear NOUN bjmsr-311 193 26 model model NOUN bjmsr-311 193 27 ( ( PUNCT bjmsr-311 193 28 16 16 NUM bjmsr-311 193 29 ) ) PUNCT bjmsr-311 193 30 . . PUNCT bjmsr-311 194 1 algorithm algorithm NOUN bjmsr-311 194 2 2 2 NUM bjmsr-311 194 3 step step NOUN bjmsr-311 194 4 0 0 NUM bjmsr-311 194 5 ) ) PUNCT bjmsr-311 194 6 select select VERB bjmsr-311 194 7 an an DET bjmsr-311 194 8 arbitrary arbitrary ADJ bjmsr-311 194 9 integer integer NOUN bjmsr-311 194 10 value value NOUN bjmsr-311 194 11 a a PRON bjmsr-311 194 12 between between ADP bjmsr-311 194 13 one one NUM bjmsr-311 194 14 to to ADP bjmsr-311 194 15 n n NOUN bjmsr-311 194 16 and and CCONJ bjmsr-311 194 17 set set VERB bjmsr-311 194 18 k1 k1 NOUN bjmsr-311 194 19 = = NOUN bjmsr-311 194 20 a. a. NOUN bjmsr-311 194 21 step step NOUN bjmsr-311 194 22 1 1 NUM bjmsr-311 194 23 ) ) PUNCT bjmsr-311 194 24 compute compute NOUN bjmsr-311 194 25 ( ( PUNCT bjmsr-311 194 26 18 18 NUM bjmsr-311 194 27 ) ) PUNCT bjmsr-311 194 28 with with ADP bjmsr-311 194 29 k1 k1 NOUN bjmsr-311 194 30 = = NOUN bjmsr-311 194 31 a. a. NOUN bjmsr-311 194 32 step step NOUN bjmsr-311 194 33 2 2 NUM bjmsr-311 194 34 ) ) PUNCT bjmsr-311 194 35 minimize minimize NOUN bjmsr-311 194 36 ( ( PUNCT bjmsr-311 194 37 21 21 NUM bjmsr-311 194 38 ) ) PUNCT bjmsr-311 194 39 by by ADP bjmsr-311 194 40 using use VERB bjmsr-311 194 41 weighted weight VERB bjmsr-311 194 42 median median ADJ bjmsr-311 194 43 procedure procedure NOUN bjmsr-311 194 44 and and CCONJ bjmsr-311 194 45 find find VERB bjmsr-311 194 46 the the DET bjmsr-311 194 47 appropriate appropriate ADJ bjmsr-311 194 48 observation observation NOUN bjmsr-311 194 49 on on ADP bjmsr-311 194 50 the the DET bjmsr-311 194 51 line line NOUN bjmsr-311 194 52 , , PUNCT bjmsr-311 194 53 namely namely ADV bjmsr-311 194 54 observation observation NOUN bjmsr-311 194 55 b. b. PROPN bjmsr-311 194 56 step step NOUN bjmsr-311 194 57 3 3 NUM bjmsr-311 194 58 ) ) PUNCT bjmsr-311 194 59 compute compute NOUN bjmsr-311 194 60 ( ( PUNCT bjmsr-311 194 61 18 18 NUM bjmsr-311 194 62 ) ) PUNCT bjmsr-311 194 63 with with ADP bjmsr-311 194 64 k1 k1 PROPN bjmsr-311 194 65 = = PROPN bjmsr-311 194 66 b. b. PROPN bjmsr-311 194 67 step step NOUN bjmsr-311 194 68 4 4 NUM bjmsr-311 194 69 ) ) PUNCT bjmsr-311 194 70 minimize minimize NOUN bjmsr-311 194 71 ( ( PUNCT bjmsr-311 194 72 21 21 NUM bjmsr-311 194 73 ) ) PUNCT bjmsr-311 194 74 and and CCONJ bjmsr-311 194 75 find find VERB bjmsr-311 194 76 that that DET bjmsr-311 194 77 observation observation NOUN bjmsr-311 194 78 on on ADP bjmsr-311 194 79 the the DET bjmsr-311 194 80 line line NOUN bjmsr-311 194 81 ; ; PUNCT bjmsr-311 194 82 observation observation NOUN bjmsr-311 194 83 c. c. PROPN bjmsr-311 194 84 step step NOUN bjmsr-311 194 85 5 5 NUM bjmsr-311 194 86 ) ) PUNCT bjmsr-311 194 87 check check NOUN bjmsr-311 194 88 if if SCONJ bjmsr-311 194 89 c c PROPN bjmsr-311 194 90 = = SYM bjmsr-311 194 91 a a NOUN bjmsr-311 194 92 , , PUNCT bjmsr-311 194 93 then then ADV bjmsr-311 194 94 ß2^=yb ß2^=yb NOUN bjmsr-311 194 95 c c NOUN bjmsr-311 194 96 / / SYM bjmsr-311 194 97 x2b x2b PROPN bjmsr-311 194 98 c c NOUN bjmsr-311 194 99 , , PUNCT bjmsr-311 194 100 ß1^=yc ß1^=yc NOUN bjmsr-311 194 101 - - PUNCT bjmsr-311 194 102 ß2^x2c ß2^x2c NUM bjmsr-311 194 103 and and CCONJ bjmsr-311 194 104 stop stop VERB bjmsr-311 194 105 . . PUNCT bjmsr-311 195 1 step step NOUN bjmsr-311 195 2 6 6 NUM bjmsr-311 195 3 ) ) PUNCT bjmsr-311 195 4 set set VERB bjmsr-311 195 5 a a DET bjmsr-311 195 6 = = NOUN bjmsr-311 195 7 b b NOUN bjmsr-311 195 8 and and CCONJ bjmsr-311 195 9 go go VERB bjmsr-311 195 10 to to PART bjmsr-311 195 11 step step VERB bjmsr-311 195 12 1 1 NUM bjmsr-311 195 13 . . PUNCT bjmsr-311 195 14 operationally operationally ADV bjmsr-311 195 15 , , PUNCT bjmsr-311 195 16 the the DET bjmsr-311 195 17 following follow VERB bjmsr-311 195 18 steps step NOUN bjmsr-311 195 19 are be AUX bjmsr-311 195 20 taken take VERB bjmsr-311 195 21 . . PUNCT bjmsr-311 196 1 program program NOUN bjmsr-311 196 2 bl1s bl1s PROPN bjmsr-311 196 3 step step VERB bjmsr-311 196 4 0 0 NUM bjmsr-311 196 5 ) ) PUNCT bjmsr-311 196 6 initialization initialization NOUN bjmsr-311 196 7 . . PUNCT bjmsr-311 197 1 parameter parameter NOUN bjmsr-311 197 2 : : PUNCT bjmsr-311 197 3 n. n. PROPN bjmsr-311 197 4 real real NOUN bjmsr-311 197 5 : : PUNCT bjmsr-311 197 6 y(n y(n PROPN bjmsr-311 197 7 ) ) PUNCT bjmsr-311 197 8 , , PUNCT bjmsr-311 197 9 x2(n x2(n PROPN bjmsr-311 197 10 ) ) PUNCT bjmsr-311 197 11 , , PUNCT bjmsr-311 197 12 z(n z(n NOUN bjmsr-311 197 13 ) ) PUNCT bjmsr-311 197 14 , , PUNCT bjmsr-311 197 15 w(n w(n PROPN bjmsr-311 197 16 ) ) PUNCT bjmsr-311 197 17 . . PUNCT bjmsr-311 198 1 copyright copyright NOUN bjmsr-311 198 2 © © PROPN bjmsr-311 198 3 cc cc PROPN bjmsr-311 198 4 - - PUNCT bjmsr-311 198 5 by by ADP bjmsr-311 198 6 - - PUNCT bjmsr-311 198 7 nc nc PROPN bjmsr-311 198 8 2019 2019 NUM bjmsr-311 198 9 , , PUNCT bjmsr-311 198 10 bjmsr bjmsr PROPN bjmsr-311 198 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 199 1 bangladesh bangladesh PROPN bjmsr-311 199 2 journal journal PROPN bjmsr-311 199 3 of of ADP bjmsr-311 199 4 multidisciplinary multidisciplinary ADJ bjmsr-311 199 5 scientific scientific ADJ bjmsr-311 199 6 research research NOUN bjmsr-311 199 7 vol vol NOUN bjmsr-311 199 8 . . PROPN bjmsr-311 199 9 1 1 NUM bjmsr-311 199 10 , , PUNCT bjmsr-311 199 11 no no INTJ bjmsr-311 199 12 . . NOUN bjmsr-311 199 13 1 1 NUM bjmsr-311 199 14 ; ; PUNCT bjmsr-311 199 15 2019 2019 NUM bjmsr-311 199 16 8 8 NUM bjmsr-311 199 17 integer integer NOUN bjmsr-311 199 18 : : PUNCT bjmsr-311 199 19 l(n l(n PROPN bjmsr-311 199 20 ) ) PUNCT bjmsr-311 199 21 . . PUNCT bjmsr-311 200 1 set set NOUN bjmsr-311 200 2 : : PUNCT bjmsr-311 200 3 k1 k1 NOUN bjmsr-311 200 4 = = NOUN bjmsr-311 200 5 arbitrary arbitrary ADJ bjmsr-311 200 6 , , PUNCT bjmsr-311 200 7 k1r=0 k1r=0 PROPN bjmsr-311 200 8 , , PUNCT bjmsr-311 200 9 k1s=0 k1s=0 PROPN bjmsr-311 200 10 , , PUNCT bjmsr-311 200 11 iter=0 iter=0 PROPN bjmsr-311 200 12 . . PUNCT bjmsr-311 201 1 read read PROPN bjmsr-311 201 2 ( ( PUNCT bjmsr-311 201 3 y(i y(i PROPN bjmsr-311 201 4 ) ) PUNCT bjmsr-311 201 5 , , PUNCT bjmsr-311 201 6 x2(i x2(i PROPN bjmsr-311 201 7 ) ) PUNCT bjmsr-311 201 8 , , PUNCT bjmsr-311 201 9 i=1,n i=1,n NOUN bjmsr-311 201 10 ) ) PUNCT bjmsr-311 201 11 step step NOUN bjmsr-311 201 12 1 1 NUM bjmsr-311 201 13 ) ) PUNCT bjmsr-311 201 14 compute compute NOUN bjmsr-311 201 15 weights weight NOUN bjmsr-311 201 16 and and CCONJ bjmsr-311 201 17 ratios ratio NOUN bjmsr-311 201 18 . . PUNCT bjmsr-311 202 1 do do AUX bjmsr-311 202 2 loop loop VERB bjmsr-311 202 3 for for ADP bjmsr-311 202 4 i=1,k1 i=1,k1 NOUN bjmsr-311 202 5 - - PUNCT bjmsr-311 202 6 1 1 NUM bjmsr-311 202 7 : : PUNCT bjmsr-311 202 8 w(i)=x2(i)-x2(k1 w(i)=x2(i)-x2(k1 PROPN bjmsr-311 202 9 ) ) PUNCT bjmsr-311 202 10 , , PUNCT bjmsr-311 202 11 z(i)=(y(i)-y(k1))/w(i z(i)=(y(i)-y(k1))/w(i NOUN bjmsr-311 202 12 ) ) PUNCT bjmsr-311 202 13 , , PUNCT bjmsr-311 202 14 end end NOUN bjmsr-311 202 15 do do VERB bjmsr-311 202 16 . . PUNCT bjmsr-311 203 1 set set NOUN bjmsr-311 203 2 : : PUNCT bjmsr-311 203 3 w(k1)=0 w(k1)=0 ADJ bjmsr-311 203 4 , , PUNCT bjmsr-311 203 5 z(k1)=0 z(k1)=0 PROPN bjmsr-311 203 6 . . PUNCT bjmsr-311 204 1 do do AUX bjmsr-311 204 2 loop loop VERB bjmsr-311 204 3 for for ADP bjmsr-311 204 4 i i PROPN bjmsr-311 204 5 = = NOUN bjmsr-311 204 6 k1 k1 X bjmsr-311 204 7 + + NOUN bjmsr-311 204 8 1,n 1,n NUM bjmsr-311 204 9 : : PUNCT bjmsr-311 204 10 w(i)=x2(i)-x2(k1 w(i)=x2(i)-x2(k1 PROPN bjmsr-311 204 11 ) ) PUNCT bjmsr-311 204 12 , , PUNCT bjmsr-311 204 13 z(i)=(y(i)-y(k1))/w(i z(i)=(y(i)-y(k1))/w(i NOUN bjmsr-311 204 14 ) ) PUNCT bjmsr-311 204 15 end end NOUN bjmsr-311 204 16 do do VERB bjmsr-311 204 17 . . PUNCT bjmsr-311 205 1 set set VERB bjmsr-311 205 2 : : PUNCT bjmsr-311 205 3 iter iter NOUN bjmsr-311 205 4 = = NOUN bjmsr-311 205 5 iter+1 iter+1 ADJ bjmsr-311 205 6 . . PUNCT bjmsr-311 206 1 step step NOUN bjmsr-311 206 2 2 2 NUM bjmsr-311 206 3 ) ) PUNCT bjmsr-311 206 4 compute compute NOUN bjmsr-311 206 5 weighted weight VERB bjmsr-311 206 6 median median NOUN bjmsr-311 206 7 . . PUNCT bjmsr-311 207 1 let let VERB bjmsr-311 207 2 : : PUNCT bjmsr-311 207 3 lm lm PROPN bjmsr-311 207 4 = = NOUN bjmsr-311 207 5 lwmed(n lwmed(n NOUN bjmsr-311 207 6 , , PUNCT bjmsr-311 207 7 z z PROPN bjmsr-311 207 8 , , PUNCT bjmsr-311 207 9 w w PROPN bjmsr-311 207 10 , , PUNCT bjmsr-311 207 11 l l NOUN bjmsr-311 207 12 ) ) PUNCT bjmsr-311 207 13 . . PUNCT bjmsr-311 208 1 step step NOUN bjmsr-311 208 2 3 3 NUM bjmsr-311 208 3 ) ) PUNCT bjmsr-311 208 4 check check NOUN bjmsr-311 208 5 for for ADP bjmsr-311 208 6 optimality optimality NOUN bjmsr-311 208 7 . . PUNCT bjmsr-311 209 1 set set NOUN bjmsr-311 209 2 : : PUNCT bjmsr-311 209 3 k1s k1s NOUN bjmsr-311 209 4 = = SYM bjmsr-311 209 5 k1r k1r NOUN bjmsr-311 209 6 , , PUNCT bjmsr-311 209 7 k1r k1r NOUN bjmsr-311 209 8 = = SYM bjmsr-311 209 9 k1 k1 NOUN bjmsr-311 209 10 . . PUNCT bjmsr-311 210 1 if if SCONJ bjmsr-311 210 2 lm lm NOUN bjmsr-311 210 3 = = NOUN bjmsr-311 210 4 k1s k1s PROPN bjmsr-311 210 5 then then ADV bjmsr-311 210 6 go go VERB bjmsr-311 210 7 to to PART bjmsr-311 210 8 step step VERB bjmsr-311 210 9 4 4 NUM bjmsr-311 210 10 , , PUNCT bjmsr-311 210 11 otherwise otherwise ADV bjmsr-311 210 12 k1 k1 X bjmsr-311 210 13 = = SYM bjmsr-311 210 14 lm lm X bjmsr-311 210 15 . . PUNCT bjmsr-311 211 1 go go VERB bjmsr-311 211 2 to to PART bjmsr-311 211 3 step step VERB bjmsr-311 211 4 1 1 NUM bjmsr-311 211 5 . . PUNCT bjmsr-311 212 1 step step NOUN bjmsr-311 212 2 4 4 NUM bjmsr-311 212 3 ) ) PUNCT bjmsr-311 212 4 compute compute VERB bjmsr-311 212 5 the the DET bjmsr-311 212 6 solution solution NOUN bjmsr-311 212 7 . . PUNCT bjmsr-311 213 1 let let VERB bjmsr-311 213 2 b2 b2 NOUN bjmsr-311 213 3 = = NOUN bjmsr-311 213 4 z(lm z(lm NOUN bjmsr-311 213 5 ) ) PUNCT bjmsr-311 213 6 , , PUNCT bjmsr-311 213 7 b1 b1 NOUN bjmsr-311 213 8 = = SYM bjmsr-311 213 9 y(k1)-b2*x2(k1 y(k1)-b2*x2(k1 PROPN bjmsr-311 213 10 ) ) PUNCT bjmsr-311 213 11 . . PUNCT bjmsr-311 214 1 print print NOUN bjmsr-311 214 2 b1 b1 PROPN bjmsr-311 214 3 , , PUNCT bjmsr-311 214 4 b2 b2 NOUN bjmsr-311 214 5 , , PUNCT bjmsr-311 214 6 k1 k1 NOUN bjmsr-311 214 7 , , PUNCT bjmsr-311 214 8 lm lm INTJ bjmsr-311 214 9 , , PUNCT bjmsr-311 214 10 iter iter PROPN bjmsr-311 214 11 . . PUNCT bjmsr-311 215 1 stop stop NOUN bjmsr-311 215 2 . . PUNCT bjmsr-311 216 1 en en ADP bjmsr-311 216 2 4 4 NUM bjmsr-311 216 3 . . PUNCT bjmsr-311 216 4 generalization generalization NOUN bjmsr-311 216 5 to to ADP bjmsr-311 216 6 m m PROPN bjmsr-311 216 7 parameters parameter NOUN bjmsr-311 216 8 now now ADV bjmsr-311 216 9 we we PRON bjmsr-311 216 10 extend extend VERB bjmsr-311 216 11 the the DET bjmsr-311 216 12 above above ADJ bjmsr-311 216 13 procedure procedure NOUN bjmsr-311 216 14 to to ADP bjmsr-311 216 15 the the DET bjmsr-311 216 16 restricted restricted ADJ bjmsr-311 216 17 two two NUM bjmsr-311 216 18 parameters parameter NOUN bjmsr-311 216 19 model model NOUN bjmsr-311 216 20 , , PUNCT bjmsr-311 216 21 namely namely ADV bjmsr-311 216 22 , , PUNCT bjmsr-311 216 23 yi yi PROPN bjmsr-311 216 24 = = NOUN bjmsr-311 216 25 ß2x2i ß2x2i NUM bjmsr-311 217 1 + + CCONJ bjmsr-311 217 2 ß3x3i ß3x3i PUNCT bjmsr-311 217 3 + + X bjmsr-311 217 4 ui ui PROPN bjmsr-311 217 5 ( ( PUNCT bjmsr-311 217 6 37 37 NUM bjmsr-311 217 7 ) ) PUNCT bjmsr-311 217 8 let let VERB bjmsr-311 217 9 , , PUNCT bjmsr-311 217 10 n n PROPN bjmsr-311 217 11 s s NOUN bjmsr-311 217 12 = = SYM bjmsr-311 217 13 σ σ PROPN bjmsr-311 217 14 │ │ NOUN bjmsr-311 217 15 yi yi PROPN bjmsr-311 217 16 ß2x2i ß2x2i NUM bjmsr-311 217 17 ß3x3i ß3x3i NUM bjmsr-311 217 18 │ │ X bjmsr-311 217 19 ( ( PUNCT bjmsr-311 217 20 38 38 NUM bjmsr-311 217 21 ) ) PUNCT bjmsr-311 217 22 i=1 i=1 ADP bjmsr-311 218 1 s s VERB bjmsr-311 218 2 can can AUX bjmsr-311 218 3 be be AUX bjmsr-311 218 4 written write VERB bjmsr-311 218 5 as as ADP bjmsr-311 218 6 , , PUNCT bjmsr-311 218 7 n n CCONJ bjmsr-311 218 8 n n PROPN bjmsr-311 218 9 s s NOUN bjmsr-311 218 10 = = PROPN bjmsr-311 218 11 σ σ PROPN bjmsr-311 218 12 │ │ NOUN bjmsr-311 218 13 x2i x2i NUM bjmsr-311 218 14 │ │ VERB bjmsr-311 218 15 │ │ NOUN bjmsr-311 218 16 yi yi NOUN bjmsr-311 218 17 / / SYM bjmsr-311 218 18 x2i x2i PROPN bjmsr-311 218 19 ß2 ß2 PROPN bjmsr-311 218 20 ß3x3i ß3x3i NUM bjmsr-311 218 21 / / SYM bjmsr-311 218 22 x2i x2i NOUN bjmsr-311 218 23 │ │ X bjmsr-311 218 24 = = SYM bjmsr-311 218 25 σ σ PROPN bjmsr-311 218 26 │ │ NOUN bjmsr-311 218 27 x2i x2i NUM bjmsr-311 218 28 │ │ ADJ bjmsr-311 218 29 │ │ NOUN bjmsr-311 218 30 yi yi NOUN bjmsr-311 218 31 s1 s1 NOUN bjmsr-311 218 32 ß2 ß2 X bjmsr-311 218 33 ß3x3i ß3x3i PUNCT bjmsr-311 218 34 s1 s1 NOUN bjmsr-311 218 35 │ │ X bjmsr-311 218 36 ( ( PUNCT bjmsr-311 218 37 39 39 NUM bjmsr-311 218 38 ) ) PUNCT bjmsr-311 218 39 i=1 i=1 VERB bjmsr-311 218 40 i=1 i=1 PROPN bjmsr-311 218 41 where where SCONJ bjmsr-311 218 42 , , PUNCT bjmsr-311 218 43 yi yi PROPN bjmsr-311 218 44 s1 s1 NOUN bjmsr-311 218 45 = = SYM bjmsr-311 218 46 yi yi PROPN bjmsr-311 218 47 / / SYM bjmsr-311 218 48 x2i x2i PROPN bjmsr-311 218 49 , , PUNCT bjmsr-311 218 50 x3i x3i PROPN bjmsr-311 219 1 s1 s1 PROPN bjmsr-311 219 2 = = PUNCT bjmsr-311 219 3 x3i x3i PROPN bjmsr-311 219 4 / / SYM bjmsr-311 219 5 x2i x2i PROPN bjmsr-311 219 6 i=1, i=1, PROPN bjmsr-311 219 7 ... ... PUNCT bjmsr-311 219 8 ,n ,n PUNCT bjmsr-311 219 9 ( ( PUNCT bjmsr-311 219 10 40 40 NUM bjmsr-311 219 11 ) ) PUNCT bjmsr-311 219 12 minimization minimization NOUN bjmsr-311 219 13 of of ADP bjmsr-311 219 14 ( ( PUNCT bjmsr-311 219 15 39 39 NUM bjmsr-311 219 16 ) ) PUNCT bjmsr-311 219 17 is be AUX bjmsr-311 219 18 similar similar ADJ bjmsr-311 219 19 to to ADP bjmsr-311 219 20 that that PRON bjmsr-311 219 21 of of ADP bjmsr-311 219 22 simple simple ADJ bjmsr-311 219 23 linear linear NOUN bjmsr-311 219 24 model model NOUN bjmsr-311 219 25 explained explain VERB bjmsr-311 219 26 in in ADP bjmsr-311 219 27 the the DET bjmsr-311 219 28 previous previous ADJ bjmsr-311 219 29 section section NOUN bjmsr-311 219 30 . . PUNCT bjmsr-311 220 1 an an DET bjmsr-311 220 2 important important ADJ bjmsr-311 220 3 distinction distinction NOUN bjmsr-311 220 4 for for ADP bjmsr-311 220 5 solving solve VERB bjmsr-311 220 6 ( ( PUNCT bjmsr-311 220 7 39 39 NUM bjmsr-311 220 8 ) ) PUNCT bjmsr-311 220 9 in in ADP bjmsr-311 220 10 comparison comparison NOUN bjmsr-311 220 11 to to ADP bjmsr-311 220 12 ( ( PUNCT bjmsr-311 220 13 17 17 NUM bjmsr-311 220 14 ) ) PUNCT bjmsr-311 220 15 is be AUX bjmsr-311 220 16 the the DET bjmsr-311 220 17 expression expression NOUN bjmsr-311 220 18 │ │ ADV bjmsr-311 220 19 x2i x2i NUM bjmsr-311 220 20 │ │ NUM bjmsr-311 220 21 which which PRON bjmsr-311 220 22 has have AUX bjmsr-311 220 23 been be AUX bjmsr-311 220 24 multiplied multiply VERB bjmsr-311 220 25 to to ADP bjmsr-311 220 26 │ │ NUM bjmsr-311 220 27 yi yi PROPN bjmsr-311 220 28 s1 s1 NOUN bjmsr-311 220 29 - - PUNCT bjmsr-311 220 30 ß2 ß2 VERB bjmsr-311 220 31 - - PUNCT bjmsr-311 220 32 ß3x3i ß3x3i X bjmsr-311 220 33 s1 s1 NOUN bjmsr-311 220 34 │ │ NUM bjmsr-311 220 35 . . PUNCT bjmsr-311 221 1 this this DET bjmsr-311 221 2 multiplication multiplication NOUN bjmsr-311 221 3 does do AUX bjmsr-311 221 4 not not PART bjmsr-311 221 5 make make VERB bjmsr-311 221 6 any any DET bjmsr-311 221 7 problem problem NOUN bjmsr-311 221 8 when when SCONJ bjmsr-311 221 9 ( ( PUNCT bjmsr-311 221 10 39 39 NUM bjmsr-311 221 11 ) ) PUNCT bjmsr-311 221 12 is be AUX bjmsr-311 221 13 minimized minimize VERB bjmsr-311 221 14 , , PUNCT bjmsr-311 221 15 because because SCONJ bjmsr-311 221 16 if if SCONJ bjmsr-311 221 17 we we PRON bjmsr-311 221 18 deviate deviate VERB bjmsr-311 221 19 y y PROPN bjmsr-311 221 20 i i PROPN bjmsr-311 221 21 s1 s1 PROPN bjmsr-311 221 22 and and CCONJ bjmsr-311 221 23 x3i x3i PROPN bjmsr-311 221 24 s1 s1 NOUN bjmsr-311 221 25 from from ADP bjmsr-311 221 26 the the DET bjmsr-311 221 27 point point NOUN bjmsr-311 221 28 k1 k1 NOUN bjmsr-311 221 29 as as ADP bjmsr-311 221 30 , , PUNCT bjmsr-311 221 31 yi yi PROPN bjmsr-311 221 32 s1k1 s1k1 DET bjmsr-311 221 33 = = NOUN bjmsr-311 221 34 yi yi NOUN bjmsr-311 221 35 s1 s1 PROPN bjmsr-311 221 36 yk1 yk1 PROPN bjmsr-311 221 37 s1 s1 PROPN bjmsr-311 221 38 , , PUNCT bjmsr-311 221 39 x3i x3i PROPN bjmsr-311 221 40 s1k1 s1k1 PRON bjmsr-311 221 41 = = SYM bjmsr-311 221 42 x3i x3i PROPN bjmsr-311 221 43 s1 s1 PROPN bjmsr-311 221 44 x3k1 x3k1 PROPN bjmsr-311 221 45 s1 s1 PROPN bjmsr-311 221 46 i=1, i=1, PROPN bjmsr-311 221 47 ... ... PUNCT bjmsr-311 221 48 ,n ,n PUNCT bjmsr-311 221 49 ( ( PUNCT bjmsr-311 221 50 41 41 NUM bjmsr-311 221 51 ) ) PUNCT bjmsr-311 221 52 then then ADV bjmsr-311 221 53 we we PRON bjmsr-311 221 54 can can AUX bjmsr-311 221 55 rewrite rewrite VERB bjmsr-311 221 56 ( ( PUNCT bjmsr-311 221 57 39 39 NUM bjmsr-311 221 58 ) ) PUNCT bjmsr-311 221 59 similar similar ADJ bjmsr-311 221 60 to to ADP bjmsr-311 221 61 ( ( PUNCT bjmsr-311 221 62 21 21 NUM bjmsr-311 221 63 ) ) PUNCT bjmsr-311 221 64 , , PUNCT bjmsr-311 221 65 so so ADV bjmsr-311 221 66 , , PUNCT bjmsr-311 221 67 n n PROPN bjmsr-311 221 68 sk1 sk1 PROPN bjmsr-311 221 69 = = PROPN bjmsr-311 221 70 σ σ PROPN bjmsr-311 221 71 │ │ NOUN bjmsr-311 221 72 x2i x2i NUM bjmsr-311 221 73 │ │ VERB bjmsr-311 221 74 │ │ NOUN bjmsr-311 221 75 yi yi NOUN bjmsr-311 221 76 s1k1 s1k1 DET bjmsr-311 221 77 ß3x3i ß3x3i X bjmsr-311 221 78 s1k1 s1k1 NOUN bjmsr-311 221 79 │ │ X bjmsr-311 221 80 ( ( PUNCT bjmsr-311 221 81 42 42 NUM bjmsr-311 221 82 ) ) PUNCT bjmsr-311 221 83 i=1 i=1 VERB bjmsr-311 221 84 to to PART bjmsr-311 221 85 minimize minimize VERB bjmsr-311 221 86 ( ( PUNCT bjmsr-311 221 87 42 42 NUM bjmsr-311 221 88 ) ) PUNCT bjmsr-311 221 89 , , PUNCT bjmsr-311 221 90 we we PRON bjmsr-311 221 91 should should AUX bjmsr-311 221 92 use use VERB bjmsr-311 221 93 the the DET bjmsr-311 221 94 following follow VERB bjmsr-311 221 95 expression expression NOUN bjmsr-311 221 96 , , PUNCT bjmsr-311 221 97 n n PROPN bjmsr-311 221 98 sk1 sk1 NOUN bjmsr-311 221 99 = = PROPN bjmsr-311 221 100 σ σ PROPN bjmsr-311 221 101 │ │ NOUN bjmsr-311 221 102 x2ix3i x2ix3i X bjmsr-311 221 103 s1k1 s1k1 NOUN bjmsr-311 221 104 │ │ ADJ bjmsr-311 221 105 │ │ ADJ bjmsr-311 221 106 yi yi NOUN bjmsr-311 221 107 s1k1 s1k1 NOUN bjmsr-311 221 108 / / SYM bjmsr-311 221 109 x3i x3i PROPN bjmsr-311 221 110 s1k1 s1k1 NUM bjmsr-311 221 111 ß3 ß3 NOUN bjmsr-311 221 112 │ │ PUNCT bjmsr-311 221 113 ( ( PUNCT bjmsr-311 221 114 43 43 NUM bjmsr-311 221 115 ) ) PUNCT bjmsr-311 221 116 i=1 i=1 VERB bjmsr-311 222 1 according accord VERB bjmsr-311 222 2 to to ADP bjmsr-311 222 3 bidabad bidabad NOUN bjmsr-311 222 4 ( ( PUNCT bjmsr-311 222 5 1987a,88a 1987a,88a NUM bjmsr-311 222 6 ) ) PUNCT bjmsr-311 222 7 , , PUNCT bjmsr-311 222 8 in in ADP bjmsr-311 222 9 applying apply VERB bjmsr-311 222 10 discrete discrete ADJ bjmsr-311 222 11 derivative derivative NOUN bjmsr-311 222 12 to to ADP bjmsr-311 222 13 ( ( PUNCT bjmsr-311 222 14 43 43 NUM bjmsr-311 222 15 ) ) PUNCT bjmsr-311 222 16 the the DET bjmsr-311 222 17 term term NOUN bjmsr-311 222 18 in in ADP bjmsr-311 222 19 the the DET bjmsr-311 222 20 first first ADJ bjmsr-311 222 21 absolute absolute ADJ bjmsr-311 222 22 value value NOUN bjmsr-311 222 23 sign sign NOUN bjmsr-311 222 24 is be AUX bjmsr-311 222 25 used use VERB bjmsr-311 222 26 to to PART bjmsr-311 222 27 find find VERB bjmsr-311 222 28 the the DET bjmsr-311 222 29 subscript subscript NOUN bjmsr-311 222 30 of of ADP bjmsr-311 222 31 that that DET bjmsr-311 222 32 point point NOUN bjmsr-311 222 33 which which PRON bjmsr-311 222 34 locates locate VERB bjmsr-311 222 35 on on ADP bjmsr-311 222 36 the the DET bjmsr-311 222 37 regression regression NOUN bjmsr-311 222 38 line line NOUN bjmsr-311 222 39 . . PUNCT bjmsr-311 223 1 in in ADP bjmsr-311 223 2 comparison comparison NOUN bjmsr-311 223 3 to to ADP bjmsr-311 223 4 the the DET bjmsr-311 223 5 simple simple ADJ bjmsr-311 223 6 unrestricted unrestricted ADJ bjmsr-311 223 7 linear linear NOUN bjmsr-311 223 8 model model NOUN bjmsr-311 223 9 ( ( PUNCT bjmsr-311 223 10 16 16 NUM bjmsr-311 223 11 ) ) PUNCT bjmsr-311 223 12 , , PUNCT bjmsr-311 223 13 this this PRON bjmsr-311 223 14 is be AUX bjmsr-311 223 15 the the DET bjmsr-311 223 16 main main ADJ bjmsr-311 223 17 difference difference NOUN bjmsr-311 223 18 . . PUNCT bjmsr-311 224 1 in in ADP bjmsr-311 224 2 the the DET bjmsr-311 224 3 case case NOUN bjmsr-311 224 4 of of ADP bjmsr-311 224 5 inclusion inclusion NOUN bjmsr-311 224 6 of of ADP bjmsr-311 224 7 an an DET bjmsr-311 224 8 intercept intercept NOUN bjmsr-311 224 9 in in ADP bjmsr-311 224 10 the the DET bjmsr-311 224 11 model model NOUN bjmsr-311 224 12 given give VERB bjmsr-311 224 13 by by ADP bjmsr-311 224 14 ( ( PUNCT bjmsr-311 224 15 37 37 NUM bjmsr-311 224 16 ) ) PUNCT bjmsr-311 224 17 , , PUNCT bjmsr-311 224 18 we we PRON bjmsr-311 224 19 have have VERB bjmsr-311 224 20 , , PUNCT bjmsr-311 224 21 n n PROPN bjmsr-311 224 22 s s NOUN bjmsr-311 224 23 = = SYM bjmsr-311 224 24 σ σ PROPN bjmsr-311 224 25 │ │ NOUN bjmsr-311 224 26 yi yi PROPN bjmsr-311 224 27 ß1 ß1 PROPN bjmsr-311 224 28 ß2x2i ß2x2i NUM bjmsr-311 224 29 ß3x3i ß3x3i NUM bjmsr-311 224 30 │ │ X bjmsr-311 224 31 ( ( PUNCT bjmsr-311 224 32 44 44 NUM bjmsr-311 224 33 ) ) PUNCT bjmsr-311 224 34 i=1 i=1 PRON bjmsr-311 225 1 let let VERB bjmsr-311 225 2 k1 k1 NOUN bjmsr-311 225 3 be be AUX bjmsr-311 225 4 an an DET bjmsr-311 225 5 arbitrary arbitrary ADJ bjmsr-311 225 6 subscript subscript NOUN bjmsr-311 225 7 then then ADV bjmsr-311 225 8 , , PUNCT bjmsr-311 225 9 the the DET bjmsr-311 225 10 transference transference NOUN bjmsr-311 225 11 of of ADP bjmsr-311 225 12 the the DET bjmsr-311 225 13 origin origin NOUN bjmsr-311 225 14 of of ADP bjmsr-311 225 15 coordinates coordinate NOUN bjmsr-311 225 16 to to ADP bjmsr-311 225 17 the the DET bjmsr-311 225 18 k1 k1 PROPN bjmsr-311 225 19 th th NOUN bjmsr-311 225 20 point point NOUN bjmsr-311 225 21 is be AUX bjmsr-311 225 22 done do VERB bjmsr-311 225 23 by by ADP bjmsr-311 225 24 deviating deviate VERB bjmsr-311 225 25 all all DET bjmsr-311 225 26 observations observation NOUN bjmsr-311 225 27 from from ADP bjmsr-311 225 28 this this DET bjmsr-311 225 29 point point NOUN bjmsr-311 225 30 , , PUNCT bjmsr-311 225 31 namely namely ADV bjmsr-311 225 32 , , PUNCT bjmsr-311 225 33 yi yi PROPN bjmsr-311 225 34 k1 k1 PROPN bjmsr-311 225 35 = = SYM bjmsr-311 225 36 yi yi PROPN bjmsr-311 225 37 yk1 yk1 PROPN bjmsr-311 225 38 , , PUNCT bjmsr-311 225 39 x2i x2i PROPN bjmsr-311 225 40 k1 k1 PROPN bjmsr-311 226 1 = = SYM bjmsr-311 226 2 x2i x2i PROPN bjmsr-311 226 3 x2k1 x2k1 PROPN bjmsr-311 226 4 , , PUNCT bjmsr-311 226 5 x3i x3i PROPN bjmsr-311 226 6 k1 k1 PROPN bjmsr-311 226 7 = = PUNCT bjmsr-311 226 8 x3i x3i PROPN bjmsr-311 226 9 -x3k1 -x3k1 PUNCT bjmsr-311 226 10 i=1, i=1, PROPN bjmsr-311 226 11 ... ... PUNCT bjmsr-311 226 12 ,n ,n PUNCT bjmsr-311 226 13 ( ( PUNCT bjmsr-311 226 14 45 45 NUM bjmsr-311 226 15 ) ) PUNCT bjmsr-311 226 16 rearrange rearrange VERB bjmsr-311 226 17 the the DET bjmsr-311 226 18 terms term NOUN bjmsr-311 226 19 of of ADP bjmsr-311 226 20 ( ( PUNCT bjmsr-311 226 21 45 45 NUM bjmsr-311 226 22 ) ) PUNCT bjmsr-311 226 23 and and CCONJ bjmsr-311 226 24 substitute substitute NOUN bjmsr-311 226 25 in in ADP bjmsr-311 226 26 ( ( PUNCT bjmsr-311 226 27 44 44 NUM bjmsr-311 226 28 ) ) PUNCT bjmsr-311 226 29 , , PUNCT bjmsr-311 226 30 then then ADV bjmsr-311 226 31 we we PRON bjmsr-311 226 32 have have VERB bjmsr-311 226 33 , , PUNCT bjmsr-311 227 1 n n DET bjmsr-311 227 2 copyright copyright NOUN bjmsr-311 227 3 © © PROPN bjmsr-311 227 4 cc cc NOUN bjmsr-311 227 5 - - PUNCT bjmsr-311 227 6 by by ADP bjmsr-311 227 7 - - PUNCT bjmsr-311 227 8 nc nc PROPN bjmsr-311 227 9 2019 2019 NUM bjmsr-311 227 10 , , PUNCT bjmsr-311 227 11 bjmsr bjmsr PROPN bjmsr-311 227 12 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 227 13 bangladesh bangladesh PROPN bjmsr-311 227 14 journal journal PROPN bjmsr-311 227 15 of of ADP bjmsr-311 227 16 multidisciplinary multidisciplinary ADJ bjmsr-311 227 17 scientific scientific ADJ bjmsr-311 227 18 research research NOUN bjmsr-311 227 19 vol vol NOUN bjmsr-311 227 20 . . PROPN bjmsr-311 228 1 1 1 NUM bjmsr-311 228 2 , , PUNCT bjmsr-311 228 3 no no INTJ bjmsr-311 228 4 . . NOUN bjmsr-311 228 5 1 1 NUM bjmsr-311 228 6 ; ; PUNCT bjmsr-311 228 7 2019 2019 NUM bjmsr-311 228 8 9 9 NUM bjmsr-311 228 9 s s NOUN bjmsr-311 228 10 = = SYM bjmsr-311 228 11 σ σ PROPN bjmsr-311 228 12 │ │ NOUN bjmsr-311 228 13 yi yi PROPN bjmsr-311 228 14 k1 k1 PROPN bjmsr-311 228 15 - - PUNCT bjmsr-311 228 16 ß2x2i ß2x2i NUM bjmsr-311 228 17 k1 k1 NOUN bjmsr-311 228 18 - - PUNCT bjmsr-311 228 19 ß3x3i ß3x3i NOUN bjmsr-311 228 20 k1+(yk1 k1+(yk1 PROPN bjmsr-311 228 21 - - PUNCT bjmsr-311 228 22 ß1 ß1 NOUN bjmsr-311 228 23 - - PUNCT bjmsr-311 228 24 ß2x2k1 ß2x2k1 NOUN bjmsr-311 228 25 - - PUNCT bjmsr-311 228 26 ß3x3k1 ß3x3k1 NOUN bjmsr-311 228 27 ) ) PUNCT bjmsr-311 228 28 │ │ X bjmsr-311 228 29 ( ( PUNCT bjmsr-311 228 30 46 46 NUM bjmsr-311 228 31 ) ) PUNCT bjmsr-311 228 32 i=1 i=1 X bjmsr-311 228 33 if if SCONJ bjmsr-311 228 34 the the DET bjmsr-311 228 35 k1th k1th PUNCT bjmsr-311 228 36 observation observation NOUN bjmsr-311 228 37 is be AUX bjmsr-311 228 38 on on ADP bjmsr-311 228 39 the the DET bjmsr-311 228 40 regression regression NOUN bjmsr-311 228 41 plane plane NOUN bjmsr-311 228 42 , , PUNCT bjmsr-311 228 43 then then ADV bjmsr-311 228 44 yk1 yk1 PROPN bjmsr-311 228 45 ß1 ß1 PROPN bjmsr-311 228 46 ß2x2k1 ß2x2k1 VERB bjmsr-311 228 47 ß3x3k1 ß3x3k1 NOUN bjmsr-311 228 48 = = SYM bjmsr-311 228 49 0 0 NUM bjmsr-311 229 1 ( ( PUNCT bjmsr-311 229 2 47 47 NUM bjmsr-311 229 3 ) ) PUNCT bjmsr-311 230 1 so so ADV bjmsr-311 230 2 , , PUNCT bjmsr-311 230 3 instead instead ADV bjmsr-311 230 4 of of ADP bjmsr-311 230 5 minimizing minimize VERB bjmsr-311 230 6 ( ( PUNCT bjmsr-311 230 7 44 44 NUM bjmsr-311 230 8 ) ) PUNCT bjmsr-311 230 9 , , PUNCT bjmsr-311 230 10 the the DET bjmsr-311 230 11 following follow VERB bjmsr-311 230 12 function function NOUN bjmsr-311 230 13 is be AUX bjmsr-311 230 14 minimized minimize VERB bjmsr-311 230 15 : : PUNCT bjmsr-311 230 16 n n PROPN bjmsr-311 230 17 sk1 sk1 PROPN bjmsr-311 230 18 = = PROPN bjmsr-311 230 19 σ σ PROPN bjmsr-311 230 20 │ │ NOUN bjmsr-311 230 21 yi yi PROPN bjmsr-311 230 22 k1 k1 NOUN bjmsr-311 230 23 ß2x2i ß2x2i NUM bjmsr-311 230 24 k1 k1 PROPN bjmsr-311 230 25 ß3x3i ß3x3i X bjmsr-311 230 26 k1 k1 NOUN bjmsr-311 230 27 │ │ X bjmsr-311 230 28 ( ( PUNCT bjmsr-311 230 29 48 48 NUM bjmsr-311 230 30 ) ) PUNCT bjmsr-311 230 31 i=1 i=1 PROPN bjmsr-311 230 32 minimization minimization NOUN bjmsr-311 230 33 of of ADP bjmsr-311 230 34 ( ( PUNCT bjmsr-311 230 35 48 48 NUM bjmsr-311 230 36 ) ) PUNCT bjmsr-311 230 37 is be AUX bjmsr-311 230 38 completely completely ADV bjmsr-311 230 39 similar similar ADJ bjmsr-311 230 40 to to ADP bjmsr-311 230 41 that that PRON bjmsr-311 230 42 of of ADP bjmsr-311 230 43 ( ( PUNCT bjmsr-311 230 44 38 38 NUM bjmsr-311 230 45 ) ) PUNCT bjmsr-311 230 46 and and CCONJ bjmsr-311 230 47 can can AUX bjmsr-311 230 48 be be AUX bjmsr-311 230 49 proceeded proceed VERB bjmsr-311 230 50 as as SCONJ bjmsr-311 230 51 follows follow VERB bjmsr-311 230 52 , , PUNCT bjmsr-311 230 53 n n CCONJ bjmsr-311 230 54 n n PROPN bjmsr-311 230 55 sk1 sk1 PROPN bjmsr-311 230 56 = = PROPN bjmsr-311 230 57 σ σ PROPN bjmsr-311 230 58 │ │ PROPN bjmsr-311 230 59 x2i x2i PROPN bjmsr-311 230 60 k1 k1 PROPN bjmsr-311 230 61 │ │ NUM bjmsr-311 230 62 │ │ NOUN bjmsr-311 230 63 yi yi NOUN bjmsr-311 230 64 k1 k1 PROPN bjmsr-311 230 65 / / SYM bjmsr-311 230 66 x2i x2i PROPN bjmsr-311 230 67 k1 k1 PROPN bjmsr-311 230 68 – – PUNCT bjmsr-311 230 69 ß2 ß2 PROPN bjmsr-311 230 70 ß3x3i ß3x3i NUM bjmsr-311 230 71 k1 k1 PROPN bjmsr-311 230 72 / / SYM bjmsr-311 230 73 x2i x2i PROPN bjmsr-311 230 74 k1 k1 PROPN bjmsr-311 230 75 │ │ PROPN bjmsr-311 230 76 = = SYM bjmsr-311 230 77 σ σ PROPN bjmsr-311 230 78 │ │ PROPN bjmsr-311 230 79 x2i x2i PROPN bjmsr-311 230 80 k1 k1 PROPN bjmsr-311 230 81 │ │ NUM bjmsr-311 230 82 │ │ NOUN bjmsr-311 230 83 yi yi NOUN bjmsr-311 230 84 s1 s1 NOUN bjmsr-311 230 85 ß2 ß2 X bjmsr-311 230 86 ß3x3i ß3x3i PUNCT bjmsr-311 230 87 s1 s1 NOUN bjmsr-311 230 88 │ │ X bjmsr-311 230 89 ( ( PUNCT bjmsr-311 230 90 49 49 NUM bjmsr-311 230 91 ) ) PUNCT bjmsr-311 230 92 i=1 i=1 VERB bjmsr-311 231 1 i=1 i=1 PROPN bjmsr-311 232 1 where where SCONJ bjmsr-311 232 2 , , PUNCT bjmsr-311 232 3 yi yi PROPN bjmsr-311 232 4 s1 s1 NOUN bjmsr-311 232 5 = = PROPN bjmsr-311 232 6 yi yi PROPN bjmsr-311 232 7 k1 k1 PROPN bjmsr-311 232 8 / / SYM bjmsr-311 232 9 x2i x2i PROPN bjmsr-311 232 10 k1 k1 PROPN bjmsr-311 232 11 , , PUNCT bjmsr-311 232 12 x3i x3i PROPN bjmsr-311 232 13 s1 s1 PROPN bjmsr-311 232 14 = = PUNCT bjmsr-311 232 15 x3i x3i PROPN bjmsr-311 232 16 k1 k1 PROPN bjmsr-311 232 17 / / SYM bjmsr-311 232 18 x2i x2i PROPN bjmsr-311 232 19 k1 k1 PROPN bjmsr-311 232 20 i=1, i=1, PROPN bjmsr-311 232 21 ... ... PUNCT bjmsr-311 232 22 ,n ,n PUNCT bjmsr-311 232 23 ( ( PUNCT bjmsr-311 232 24 50 50 NUM bjmsr-311 232 25 ) ) PUNCT bjmsr-311 232 26 now now ADV bjmsr-311 232 27 , , PUNCT bjmsr-311 232 28 again again ADV bjmsr-311 232 29 , , PUNCT bjmsr-311 232 30 transfer transfer VERB bjmsr-311 232 31 the the DET bjmsr-311 232 32 origin origin NOUN bjmsr-311 232 33 of of ADP bjmsr-311 232 34 the the DET bjmsr-311 232 35 two two NUM bjmsr-311 232 36 dimensional dimensional ADJ bjmsr-311 232 37 ys1xx3 ys1xx3 NOUN bjmsr-311 232 38 s1 s1 PROPN bjmsr-311 232 39 coordinates coordinate NOUN bjmsr-311 232 40 to to ADP bjmsr-311 232 41 an an DET bjmsr-311 232 42 arbitrary arbitrary ADJ bjmsr-311 232 43 point point NOUN bjmsr-311 232 44 k2 k2 NOUN bjmsr-311 232 45 by by ADP bjmsr-311 232 46 deviating deviate VERB bjmsr-311 232 47 yi yi NOUN bjmsr-311 232 48 s1 s1 PROPN bjmsr-311 232 49 and and CCONJ bjmsr-311 232 50 x3i x3i PROPN bjmsr-311 232 51 s1 s1 PROPN bjmsr-311 232 52 from from ADP bjmsr-311 232 53 yk2 yk2 NOUN bjmsr-311 232 54 s1 s1 PROPN bjmsr-311 232 55 and and CCONJ bjmsr-311 232 56 x3k2 x3k2 DET bjmsr-311 232 57 s1 s1 NOUN bjmsr-311 232 58 as as SCONJ bjmsr-311 232 59 follows follow VERB bjmsr-311 232 60 , , PUNCT bjmsr-311 233 1 yi yi X bjmsr-311 233 2 s1k2 s1k2 NOUN bjmsr-311 233 3 = = SYM bjmsr-311 233 4 yi yi PROPN bjmsr-311 233 5 s1 s1 PROPN bjmsr-311 233 6 yk2 yk2 PROPN bjmsr-311 233 7 s1 s1 PROPN bjmsr-311 233 8 , , PUNCT bjmsr-311 233 9 x3i x3i PROPN bjmsr-311 234 1 s1k2 s1k2 PROPN bjmsr-311 234 2 = = SYM bjmsr-311 234 3 x3i x3i PROPN bjmsr-311 235 1 s1 s1 PROPN bjmsr-311 235 2 x3k2 x3k2 PROPN bjmsr-311 235 3 s1 s1 PROPN bjmsr-311 235 4 i=1, i=1, PROPN bjmsr-311 235 5 ... ... PUNCT bjmsr-311 235 6 ,n ,n PUNCT bjmsr-311 235 7 ( ( PUNCT bjmsr-311 235 8 51 51 NUM bjmsr-311 235 9 ) ) PUNCT bjmsr-311 235 10 by by ADP bjmsr-311 235 11 rearranging rearrange VERB bjmsr-311 235 12 the the DET bjmsr-311 235 13 terms term NOUN bjmsr-311 235 14 of of ADP bjmsr-311 235 15 ( ( PUNCT bjmsr-311 235 16 51 51 NUM bjmsr-311 235 17 ) ) PUNCT bjmsr-311 235 18 and and CCONJ bjmsr-311 235 19 substituting substitute VERB bjmsr-311 235 20 them they PRON bjmsr-311 235 21 into into ADP bjmsr-311 235 22 ( ( PUNCT bjmsr-311 235 23 49 49 NUM bjmsr-311 235 24 ) ) PUNCT bjmsr-311 235 25 and and CCONJ bjmsr-311 235 26 assuming assume VERB bjmsr-311 235 27 that that SCONJ bjmsr-311 235 28 the the DET bjmsr-311 235 29 point point NOUN bjmsr-311 235 30 k2 k2 PROPN bjmsr-311 235 31 is be AUX bjmsr-311 235 32 on on ADP bjmsr-311 235 33 the the DET bjmsr-311 235 34 regression regression NOUN bjmsr-311 235 35 plane plane NOUN bjmsr-311 235 36 , , PUNCT bjmsr-311 235 37 we we PRON bjmsr-311 235 38 can can AUX bjmsr-311 235 39 rewrite rewrite VERB bjmsr-311 235 40 ( ( PUNCT bjmsr-311 235 41 49 49 NUM bjmsr-311 235 42 ) ) PUNCT bjmsr-311 235 43 as as ADP bjmsr-311 235 44 , , PUNCT bjmsr-311 235 45 n n PRON bjmsr-311 235 46 sk1k2 sk1k2 PROPN bjmsr-311 235 47 = = PROPN bjmsr-311 235 48 σ σ PROPN bjmsr-311 235 49 │ │ PROPN bjmsr-311 235 50 x2i x2i PROPN bjmsr-311 235 51 k1 k1 PROPN bjmsr-311 235 52 │ │ VERB bjmsr-311 235 53 │ │ NOUN bjmsr-311 235 54 yi yi NOUN bjmsr-311 235 55 s1k2 s1k2 X bjmsr-311 235 56 ß3x3i ß3x3i X bjmsr-311 235 57 s1k2 s1k2 NOUN bjmsr-311 235 58 │ │ X bjmsr-311 235 59 ( ( PUNCT bjmsr-311 235 60 52 52 NUM bjmsr-311 235 61 ) ) PUNCT bjmsr-311 235 62 i=1 i=1 PROPN bjmsr-311 235 63 or or CCONJ bjmsr-311 235 64 , , PUNCT bjmsr-311 235 65 n n PRON bjmsr-311 235 66 sk1k2 sk1k2 PROPN bjmsr-311 235 67 = = PROPN bjmsr-311 235 68 σ σ PROPN bjmsr-311 235 69 │ │ PROPN bjmsr-311 235 70 x2i x2i PROPN bjmsr-311 235 71 k1x3i k1x3i X bjmsr-311 235 72 s1k2 s1k2 NOUN bjmsr-311 235 73 │ │ VERB bjmsr-311 235 74 │ │ ADJ bjmsr-311 235 75 yi yi NOUN bjmsr-311 235 76 s1k2 s1k2 PROPN bjmsr-311 235 77 / / SYM bjmsr-311 235 78 x3i x3i PROPN bjmsr-311 236 1 s1k2 s1k2 NOUN bjmsr-311 236 2 ß3 ß3 PROPN bjmsr-311 236 3 │ │ X bjmsr-311 236 4 ( ( PUNCT bjmsr-311 236 5 53 53 NUM bjmsr-311 236 6 ) ) PUNCT bjmsr-311 236 7 i=1 i=1 ADP bjmsr-311 237 1 the the DET bjmsr-311 237 2 objective objective ADJ bjmsr-311 237 3 function function NOUN bjmsr-311 237 4 ( ( PUNCT bjmsr-311 237 5 53 53 NUM bjmsr-311 237 6 ) ) PUNCT bjmsr-311 237 7 can can AUX bjmsr-311 237 8 be be AUX bjmsr-311 237 9 minimized minimize VERB bjmsr-311 237 10 , , PUNCT bjmsr-311 237 11 as as SCONJ bjmsr-311 237 12 suggested suggest VERB bjmsr-311 237 13 before before ADV bjmsr-311 237 14 . . PUNCT bjmsr-311 238 1 now now ADV bjmsr-311 238 2 , , PUNCT bjmsr-311 238 3 the the DET bjmsr-311 238 4 procedure procedure NOUN bjmsr-311 238 5 from from ADP bjmsr-311 238 6 ( ( PUNCT bjmsr-311 238 7 49 49 NUM bjmsr-311 238 8 ) ) PUNCT bjmsr-311 238 9 to to ADP bjmsr-311 238 10 ( ( PUNCT bjmsr-311 238 11 53 53 NUM bjmsr-311 238 12 ) ) PUNCT bjmsr-311 238 13 can can AUX bjmsr-311 238 14 be be AUX bjmsr-311 238 15 repeated repeat VERB bjmsr-311 238 16 with with ADP bjmsr-311 238 17 different different ADJ bjmsr-311 238 18 values value NOUN bjmsr-311 238 19 of of ADP bjmsr-311 238 20 k2 k2 NOUN bjmsr-311 238 21 as as ADP bjmsr-311 238 22 in in ADP bjmsr-311 238 23 algorithm algorithm NOUN bjmsr-311 238 24 2 2 NUM bjmsr-311 238 25 proposed propose VERB bjmsr-311 238 26 for for ADP bjmsr-311 238 27 the the DET bjmsr-311 238 28 simple simple ADJ bjmsr-311 238 29 linear linear PROPN bjmsr-311 238 30 model model NOUN bjmsr-311 238 31 . . PUNCT bjmsr-311 239 1 when when SCONJ bjmsr-311 239 2 the the DET bjmsr-311 239 3 last last ADJ bjmsr-311 239 4 point point NOUN bjmsr-311 239 5 ( ( PUNCT bjmsr-311 239 6 m m NOUN bjmsr-311 239 7 ) ) PUNCT bjmsr-311 239 8 in in ADP bjmsr-311 239 9 the the DET bjmsr-311 239 10 process process NOUN bjmsr-311 239 11 of of ADP bjmsr-311 239 12 minimizing minimize VERB bjmsr-311 239 13 ( ( PUNCT bjmsr-311 239 14 53 53 NUM bjmsr-311 239 15 ) ) PUNCT bjmsr-311 239 16 is be AUX bjmsr-311 239 17 reached reach VERB bjmsr-311 239 18 , , PUNCT bjmsr-311 239 19 the the DET bjmsr-311 239 20 origin origin NOUN bjmsr-311 239 21 of of ADP bjmsr-311 239 22 three three NUM bjmsr-311 239 23 dimensional dimensional ADJ bjmsr-311 239 24 yxx2xx3 yxx2xx3 PROPN bjmsr-311 239 25 coordinates coordinate NOUN bjmsr-311 239 26 ( ( PUNCT bjmsr-311 239 27 k1 k1 PROPN bjmsr-311 239 28 ) ) PUNCT bjmsr-311 239 29 is be AUX bjmsr-311 239 30 transferred transfer VERB bjmsr-311 239 31 to to ADP bjmsr-311 239 32 this this DET bjmsr-311 239 33 newly newly ADV bjmsr-311 239 34 found find VERB bjmsr-311 239 35 point point NOUN bjmsr-311 239 36 m m ADJ bjmsr-311 239 37 and and CCONJ bjmsr-311 239 38 the the DET bjmsr-311 239 39 procedure procedure NOUN bjmsr-311 239 40 from from ADP bjmsr-311 239 41 ( ( PUNCT bjmsr-311 239 42 45 45 NUM bjmsr-311 239 43 ) ) PUNCT bjmsr-311 239 44 to to ADP bjmsr-311 239 45 ( ( PUNCT bjmsr-311 239 46 53 53 NUM bjmsr-311 239 47 ) ) PUNCT bjmsr-311 239 48 is be AUX bjmsr-311 239 49 again again ADV bjmsr-311 239 50 repeated repeat VERB bjmsr-311 239 51 with with ADP bjmsr-311 239 52 the the DET bjmsr-311 239 53 exception exception NOUN bjmsr-311 239 54 that that PRON bjmsr-311 239 55 instead instead ADV bjmsr-311 239 56 of of ADP bjmsr-311 239 57 assigning assign VERB bjmsr-311 239 58 an an DET bjmsr-311 239 59 arbitrary arbitrary ADJ bjmsr-311 239 60 value value NOUN bjmsr-311 239 61 to to ADP bjmsr-311 239 62 k2 k2 NOUN bjmsr-311 239 63 , , PUNCT bjmsr-311 239 64 we we PRON bjmsr-311 239 65 set set VERB bjmsr-311 239 66 k2 k2 PROPN bjmsr-311 239 67 equal equal ADJ bjmsr-311 239 68 to to ADP bjmsr-311 239 69 the the DET bjmsr-311 239 70 previous previous ADJ bjmsr-311 239 71 value value NOUN bjmsr-311 239 72 of of ADP bjmsr-311 239 73 k1 k1 NOUN bjmsr-311 239 74 . . PUNCT bjmsr-311 240 1 this this DET bjmsr-311 240 2 procedure procedure NOUN bjmsr-311 240 3 continues continue VERB bjmsr-311 240 4 until until SCONJ bjmsr-311 240 5 the the DET bjmsr-311 240 6 point point NOUN bjmsr-311 240 7 found find VERB bjmsr-311 240 8 by by ADP bjmsr-311 240 9 minimizing minimize VERB bjmsr-311 240 10 ( ( PUNCT bjmsr-311 240 11 53 53 NUM bjmsr-311 240 12 ) ) PUNCT bjmsr-311 240 13 is be AUX bjmsr-311 240 14 equal equal ADJ bjmsr-311 240 15 to to ADP bjmsr-311 240 16 the the DET bjmsr-311 240 17 previous previous ADJ bjmsr-311 240 18 value value NOUN bjmsr-311 240 19 of of ADP bjmsr-311 240 20 k1 k1 NOUN bjmsr-311 240 21 . . PUNCT bjmsr-311 241 1 the the DET bjmsr-311 241 2 values value NOUN bjmsr-311 241 3 of of ADP bjmsr-311 241 4 ß1^ ß1^ NOUN bjmsr-311 241 5 , , PUNCT bjmsr-311 241 6 ß2^ ß2^ NOUN bjmsr-311 241 7 and and CCONJ bjmsr-311 241 8 ß3^ ß3^ NUM bjmsr-311 241 9 can can AUX bjmsr-311 241 10 be be AUX bjmsr-311 241 11 computed compute VERB bjmsr-311 241 12 according accord VERB bjmsr-311 241 13 to to ADP bjmsr-311 241 14 the the DET bjmsr-311 241 15 following follow VERB bjmsr-311 241 16 formulas formula NOUN bjmsr-311 241 17 , , PUNCT bjmsr-311 241 18 ß3^ ß3^ PROPN bjmsr-311 241 19 = = NOUN bjmsr-311 241 20 ym ym NUM bjmsr-311 241 21 s1k2 s1k2 PROPN bjmsr-311 241 22 / / SYM bjmsr-311 241 23 x3 x3 ADJ bjmsr-311 241 24 m m PROPN bjmsr-311 241 25 s1k2 s1k2 NOUN bjmsr-311 241 26 , , PUNCT bjmsr-311 241 27 2^ 2^ NUM bjmsr-311 241 28 = = SYM bjmsr-311 241 29 yk2 yk2 VERB bjmsr-311 241 30 s1 s1 PROPN bjmsr-311 241 31 ß3^x3k2 ß3^x3k2 PROPN bjmsr-311 241 32 s1 s1 NOUN bjmsr-311 241 33 , , PUNCT bjmsr-311 241 34 ß1^ ß1^ NOUN bjmsr-311 241 35 = = SYM bjmsr-311 241 36 yk1 yk1 NOUN bjmsr-311 241 37 ß2^x2k1 ß2^x2k1 PROPN bjmsr-311 241 38 ß3^x3k1 ß3^x3k1 NOUN bjmsr-311 241 39 ( ( PUNCT bjmsr-311 241 40 54 54 NUM bjmsr-311 241 41 ) ) PUNCT bjmsr-311 241 42 it it PRON bjmsr-311 241 43 should should AUX bjmsr-311 241 44 be be AUX bjmsr-311 241 45 noted note VERB bjmsr-311 241 46 that that SCONJ bjmsr-311 241 47 at at ADP bjmsr-311 241 48 each each DET bjmsr-311 241 49 step step NOUN bjmsr-311 241 50 , , PUNCT bjmsr-311 241 51 it it PRON bjmsr-311 241 52 can can AUX bjmsr-311 241 53 be be AUX bjmsr-311 241 54 proved prove VERB bjmsr-311 241 55 that that SCONJ bjmsr-311 241 56 we we PRON bjmsr-311 241 57 are be AUX bjmsr-311 241 58 getting get VERB bjmsr-311 241 59 closer close ADJ bjmsr-311 241 60 to to ADP bjmsr-311 241 61 the the DET bjmsr-311 241 62 minimum minimum NOUN bjmsr-311 241 63 of of ADP bjmsr-311 241 64 s s PRON bjmsr-311 241 65 in in ADP bjmsr-311 241 66 ( ( PUNCT bjmsr-311 241 67 44 44 NUM bjmsr-311 241 68 ) ) PUNCT bjmsr-311 241 69 . . PUNCT bjmsr-311 242 1 the the DET bjmsr-311 242 2 proof proof NOUN bjmsr-311 242 3 is be AUX bjmsr-311 242 4 similar similar ADJ bjmsr-311 242 5 to to ADP bjmsr-311 242 6 that that PRON bjmsr-311 242 7 of of ADP bjmsr-311 242 8 the the DET bjmsr-311 242 9 two two NUM bjmsr-311 242 10 parameters parameter NOUN bjmsr-311 242 11 model model NOUN bjmsr-311 242 12 given give VERB bjmsr-311 242 13 by by ADP bjmsr-311 242 14 ( ( PUNCT bjmsr-311 242 15 16 16 NUM bjmsr-311 242 16 ) ) PUNCT bjmsr-311 242 17 . . PUNCT bjmsr-311 243 1 it it PRON bjmsr-311 243 2 can can AUX bjmsr-311 243 3 be be AUX bjmsr-311 243 4 shown show VERB bjmsr-311 243 5 that that SCONJ bjmsr-311 243 6 for for ADP bjmsr-311 243 7 any any DET bjmsr-311 243 8 two two NUM bjmsr-311 243 9 arbitrary arbitrary ADJ bjmsr-311 243 10 points point NOUN bjmsr-311 243 11 k1 k1 NOUN bjmsr-311 243 12 and and CCONJ bjmsr-311 243 13 k2 k2 NOUN bjmsr-311 243 14 , , PUNCT bjmsr-311 243 15 the the DET bjmsr-311 243 16 value value NOUN bjmsr-311 243 17 of of ADP bjmsr-311 243 18 sk1k2 sk1k2 PROPN bjmsr-311 243 19 given give VERB bjmsr-311 243 20 by by ADP bjmsr-311 243 21 ( ( PUNCT bjmsr-311 243 22 53 53 NUM bjmsr-311 243 23 ) ) PUNCT bjmsr-311 243 24 for for ADP bjmsr-311 243 25 any any DET bjmsr-311 243 26 commutation commutation NOUN bjmsr-311 243 27 for for ADP bjmsr-311 243 28 k1 k1 NOUN bjmsr-311 243 29 and and CCONJ bjmsr-311 243 30 k2 k2 NOUN bjmsr-311 243 31 remains remain VERB bjmsr-311 243 32 unchanged unchanged ADJ bjmsr-311 243 33 . . PUNCT bjmsr-311 244 1 this this PRON bjmsr-311 244 2 will will AUX bjmsr-311 244 3 be be AUX bjmsr-311 244 4 shown show VERB bjmsr-311 244 5 in in ADP bjmsr-311 244 6 the the DET bjmsr-311 244 7 next next ADJ bjmsr-311 244 8 sections section NOUN bjmsr-311 244 9 . . PUNCT bjmsr-311 245 1 however however ADV bjmsr-311 245 2 , , PUNCT bjmsr-311 245 3 sk1k2 sk1k2 PROPN bjmsr-311 245 4 = = SYM bjmsr-311 245 5 sk2k1 sk2k1 PROPN bjmsr-311 245 6 ( ( PUNCT bjmsr-311 245 7 55 55 NUM bjmsr-311 245 8 ) ) PUNCT bjmsr-311 245 9 now now ADV bjmsr-311 245 10 , , PUNCT bjmsr-311 245 11 following follow VERB bjmsr-311 245 12 the the DET bjmsr-311 245 13 procedure procedure NOUN bjmsr-311 245 14 of of ADP bjmsr-311 245 15 the the DET bjmsr-311 245 16 proof proof NOUN bjmsr-311 245 17 given give VERB bjmsr-311 245 18 by by ADP bjmsr-311 245 19 ( ( PUNCT bjmsr-311 245 20 28 28 NUM bjmsr-311 245 21 ) ) PUNCT bjmsr-311 245 22 through through ADP bjmsr-311 245 23 ( ( PUNCT bjmsr-311 245 24 36 36 NUM bjmsr-311 245 25 ) ) PUNCT bjmsr-311 245 26 , , PUNCT bjmsr-311 245 27 we we PRON bjmsr-311 245 28 can can AUX bjmsr-311 245 29 write write VERB bjmsr-311 245 30 , , PUNCT bjmsr-311 245 31 sk1a sk1a PROPN bjmsr-311 245 32 * * PUNCT bjmsr-311 245 33 = = PUNCT bjmsr-311 245 34 sk1b sk1b PROPN bjmsr-311 245 35 │ │ X bjmsr-311 245 36 ( ( PUNCT bjmsr-311 245 37 56 56 NUM bjmsr-311 245 38 ) ) PUNCT bjmsr-311 245 39 │ │ NOUN bjmsr-311 245 40 ß3 ß3 NOUN bjmsr-311 245 41 = = NOUN bjmsr-311 245 42 ß3 ß3 NOUN bjmsr-311 245 43 k1a k1a PROPN bjmsr-311 245 44 where where SCONJ bjmsr-311 245 45 sk1a sk1a PROPN bjmsr-311 245 46 * * PROPN bjmsr-311 245 47 denotes denote VERB bjmsr-311 245 48 the the DET bjmsr-311 245 49 optimal optimal ADJ bjmsr-311 245 50 value value NOUN bjmsr-311 245 51 of of ADP bjmsr-311 245 52 sk1a sk1a ADJ bjmsr-311 245 53 with with ADP bjmsr-311 245 54 respect respect NOUN bjmsr-311 245 55 to to ADP bjmsr-311 245 56 ß3 ß3 PROPN bjmsr-311 245 57 of of ADP bjmsr-311 245 58 ( ( PUNCT bjmsr-311 245 59 53 53 NUM bjmsr-311 245 60 ) ) PUNCT bjmsr-311 245 61 for for ADP bjmsr-311 245 62 any any DET bjmsr-311 245 63 arbitrary arbitrary ADJ bjmsr-311 245 64 integer integer NOUN bjmsr-311 245 65 a a PRON bjmsr-311 245 66 from from ADP bjmsr-311 245 67 one one NUM bjmsr-311 245 68 to to ADP bjmsr-311 245 69 n n CCONJ bjmsr-311 245 70 , , PUNCT bjmsr-311 245 71 namely namely ADV bjmsr-311 245 72 , , PUNCT bjmsr-311 245 73 sk1a sk1a PROPN bjmsr-311 245 74 * * PUNCT bjmsr-311 245 75 = = SYM bjmsr-311 245 76 min min PROPN bjmsr-311 245 77 ( ( PUNCT bjmsr-311 245 78 sk1a sk1a PROPN bjmsr-311 245 79 ) ) PUNCT bjmsr-311 245 80 ( ( PUNCT bjmsr-311 245 81 57 57 NUM bjmsr-311 245 82 ) ) PUNCT bjmsr-311 245 83 ß3 ß3 NOUN bjmsr-311 245 84 subscript subscript NOUN bjmsr-311 245 85 b b PROPN bjmsr-311 245 86 in in ADP bjmsr-311 245 87 ( ( PUNCT bjmsr-311 245 88 56 56 NUM bjmsr-311 245 89 ) ) PUNCT bjmsr-311 245 90 denotes denote VERB bjmsr-311 245 91 the the DET bjmsr-311 245 92 observation observation NOUN bjmsr-311 245 93 which which PRON bjmsr-311 245 94 is be AUX bjmsr-311 245 95 found find VERB bjmsr-311 245 96 by by ADP bjmsr-311 245 97 minimizing minimize VERB bjmsr-311 245 98 sk1a sk1a PROPN bjmsr-311 245 99 . . PUNCT bjmsr-311 246 1 since since SCONJ bjmsr-311 246 2 the the DET bjmsr-311 246 3 ath ath NOUN bjmsr-311 246 4 and and CCONJ bjmsr-311 246 5 bth bth PROPN bjmsr-311 246 6 observations observation NOUN bjmsr-311 246 7 both both PRON bjmsr-311 246 8 are be AUX bjmsr-311 246 9 on on ADP bjmsr-311 246 10 the the DET bjmsr-311 246 11 regression regression NOUN bjmsr-311 246 12 hyperplane hyperplane NOUN bjmsr-311 246 13 , , PUNCT bjmsr-311 246 14 by by ADP bjmsr-311 246 15 a a DET bjmsr-311 246 16 similar similar ADJ bjmsr-311 246 17 discussion discussion NOUN bjmsr-311 246 18 stated state VERB bjmsr-311 246 19 by by ADP bjmsr-311 246 20 ( ( PUNCT bjmsr-311 246 21 28 28 NUM bjmsr-311 246 22 ) ) PUNCT bjmsr-311 246 23 through through ADP bjmsr-311 246 24 ( ( PUNCT bjmsr-311 246 25 32 32 NUM bjmsr-311 246 26 ) ) PUNCT bjmsr-311 246 27 we we PRON bjmsr-311 246 28 can can AUX bjmsr-311 246 29 conclude conclude VERB bjmsr-311 246 30 that that PRON bjmsr-311 246 31 sk1a sk1a NOUN bjmsr-311 246 32 * * PUNCT bjmsr-311 246 33 is be AUX bjmsr-311 246 34 equal equal ADJ bjmsr-311 246 35 to to ADP bjmsr-311 246 36 sk1b sk1b PROPN bjmsr-311 246 37 which which PRON bjmsr-311 246 38 evaluated evaluate VERB bjmsr-311 246 39 at at ADP bjmsr-311 246 40 that that DET bjmsr-311 246 41 value value NOUN bjmsr-311 246 42 of of ADP bjmsr-311 246 43 ß3 ß3 NOUN bjmsr-311 246 44 which which PRON bjmsr-311 246 45 is be AUX bjmsr-311 246 46 found find VERB bjmsr-311 246 47 by by ADP bjmsr-311 246 48 minimizing minimize VERB bjmsr-311 246 49 sk1a sk1a PROPN bjmsr-311 246 50 . . PUNCT bjmsr-311 247 1 since since SCONJ bjmsr-311 247 2 the the DET bjmsr-311 247 3 left left ADJ bjmsr-311 247 4 - - PUNCT bjmsr-311 247 5 hand hand NOUN bjmsr-311 247 6 side side NOUN bjmsr-311 247 7 of of ADP bjmsr-311 247 8 ( ( PUNCT bjmsr-311 247 9 56 56 NUM bjmsr-311 247 10 ) ) PUNCT bjmsr-311 247 11 is be AUX bjmsr-311 247 12 minimum minimum ADJ bjmsr-311 247 13 and and CCONJ bjmsr-311 247 14 its its PRON bjmsr-311 247 15 right right ADJ bjmsr-311 247 16 - - PUNCT bjmsr-311 247 17 hand hand NOUN bjmsr-311 247 18 side side NOUN bjmsr-311 247 19 can can AUX bjmsr-311 247 20 be be AUX bjmsr-311 247 21 decreased decrease VERB bjmsr-311 247 22 by by ADP bjmsr-311 247 23 other other ADJ bjmsr-311 247 24 values value NOUN bjmsr-311 247 25 of of ADP bjmsr-311 247 26 ß3 ß3 NOUN bjmsr-311 247 27 , , PUNCT bjmsr-311 247 28 it it PRON bjmsr-311 247 29 can can AUX bjmsr-311 247 30 be be AUX bjmsr-311 247 31 concluded conclude VERB bjmsr-311 247 32 that that SCONJ bjmsr-311 247 33 , , PUNCT bjmsr-311 247 34 sk1a sk1a PROPN bjmsr-311 247 35 * * X bjmsr-311 247 36 > > X bjmsr-311 247 37 sk1b sk1b PROPN bjmsr-311 247 38 * * PROPN bjmsr-311 247 39 ( ( PUNCT bjmsr-311 247 40 58 58 NUM bjmsr-311 247 41 ) ) PUNCT bjmsr-311 247 42 according accord VERB bjmsr-311 247 43 to to ADP bjmsr-311 247 44 ( ( PUNCT bjmsr-311 247 45 55 55 NUM bjmsr-311 247 46 ) ) PUNCT bjmsr-311 247 47 we we PRON bjmsr-311 247 48 can can AUX bjmsr-311 247 49 write write VERB bjmsr-311 247 50 , , PUNCT bjmsr-311 247 51 sk1a sk1a PROPN bjmsr-311 247 52 * * X bjmsr-311 247 53 > > X bjmsr-311 247 54 sk1b sk1b PROPN bjmsr-311 247 55 * * PROPN bjmsr-311 247 56 = = PROPN bjmsr-311 247 57 sbk1 sbk1 PROPN bjmsr-311 247 58 * * PROPN bjmsr-311 247 59 ( ( PUNCT bjmsr-311 247 60 59 59 NUM bjmsr-311 247 61 ) ) PUNCT bjmsr-311 247 62 since since SCONJ bjmsr-311 247 63 in in ADP bjmsr-311 247 64 each each DET bjmsr-311 247 65 step step NOUN bjmsr-311 247 66 we we PRON bjmsr-311 247 67 discard discard VERB bjmsr-311 247 68 an an DET bjmsr-311 247 69 observation observation NOUN bjmsr-311 247 70 from from ADP bjmsr-311 247 71 the the DET bjmsr-311 247 72 basis basis NOUN bjmsr-311 247 73 and and CCONJ bjmsr-311 247 74 replace replace VERB bjmsr-311 247 75 it it PRON bjmsr-311 247 76 with with ADP bjmsr-311 247 77 the the DET bjmsr-311 247 78 newly newly ADV bjmsr-311 247 79 found find VERB bjmsr-311 247 80 one one NUM bjmsr-311 247 81 , , PUNCT bjmsr-311 247 82 we we PRON bjmsr-311 247 83 have have AUX bjmsr-311 247 84 , , PUNCT bjmsr-311 247 85 sk1a sk1a PROPN bjmsr-311 247 86 * * X bjmsr-311 247 87 > > X bjmsr-311 247 88 sk1b sk1b PROPN bjmsr-311 247 89 * * PROPN bjmsr-311 247 90 = = PROPN bjmsr-311 247 91 sbk1 sbk1 PROPN bjmsr-311 247 92 * * PUNCT bjmsr-311 247 93 > > X bjmsr-311 247 94 sbc sbc PROPN bjmsr-311 247 95 * * PROPN bjmsr-311 247 96 = = SYM bjmsr-311 247 97 scd scd PROPN bjmsr-311 247 98 * * PUNCT bjmsr-311 247 99 ( ( PUNCT bjmsr-311 247 100 60 60 NUM bjmsr-311 247 101 ) ) PUNCT bjmsr-311 247 102 or or CCONJ bjmsr-311 247 103 generally generally ADV bjmsr-311 247 104 , , PUNCT bjmsr-311 247 105 sk1a sk1a PROPN bjmsr-311 247 106 * * X bjmsr-311 247 107 > > X bjmsr-311 247 108 sk1b sk1b PROPN bjmsr-311 247 109 * * PROPN bjmsr-311 247 110 > > X bjmsr-311 247 111 sbc sbc PROPN bjmsr-311 247 112 * * PUNCT bjmsr-311 247 113 > > X bjmsr-311 247 114 scd scd PROPN bjmsr-311 247 115 * * PROPN bjmsr-311 247 116 ( ( PUNCT bjmsr-311 247 117 61 61 NUM bjmsr-311 247 118 ) ) PUNCT bjmsr-311 247 119 copyright copyright NOUN bjmsr-311 248 1 © © PROPN bjmsr-311 248 2 cc cc PROPN bjmsr-311 248 3 - - PUNCT bjmsr-311 248 4 by by ADP bjmsr-311 248 5 - - PUNCT bjmsr-311 248 6 nc nc PROPN bjmsr-311 248 7 2019 2019 NUM bjmsr-311 248 8 , , PUNCT bjmsr-311 248 9 bjmsr bjmsr PROPN bjmsr-311 248 10 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 248 11 bangladesh bangladesh PROPN bjmsr-311 248 12 journal journal PROPN bjmsr-311 248 13 of of ADP bjmsr-311 248 14 multidisciplinary multidisciplinary ADJ bjmsr-311 248 15 scientific scientific ADJ bjmsr-311 248 16 research research NOUN bjmsr-311 248 17 vol vol NOUN bjmsr-311 248 18 . . PROPN bjmsr-311 249 1 1 1 NUM bjmsr-311 249 2 , , PUNCT bjmsr-311 249 3 no no INTJ bjmsr-311 249 4 . . NOUN bjmsr-311 249 5 1 1 NUM bjmsr-311 249 6 ; ; PUNCT bjmsr-311 249 7 2019 2019 NUM bjmsr-311 249 8 10 10 NUM bjmsr-311 249 9 the the DET bjmsr-311 249 10 minimum minimum ADJ bjmsr-311 249 11 solution solution NOUN bjmsr-311 249 12 s s PART bjmsr-311 249 13 * * VERB bjmsr-311 249 14 is be AUX bjmsr-311 249 15 reached reach VERB bjmsr-311 249 16 when when SCONJ bjmsr-311 249 17 by by ADP bjmsr-311 249 18 entering enter VERB bjmsr-311 249 19 the the DET bjmsr-311 249 20 f f X bjmsr-311 249 21 th th PRON bjmsr-311 249 22 observation observation NOUN bjmsr-311 249 23 in in ADP bjmsr-311 249 24 the the DET bjmsr-311 249 25 basis basis NOUN bjmsr-311 249 26 we we PRON bjmsr-311 249 27 can can AUX bjmsr-311 249 28 not not PART bjmsr-311 249 29 reduce reduce VERB bjmsr-311 249 30 the the DET bjmsr-311 249 31 objective objective ADJ bjmsr-311 249 32 function function NOUN bjmsr-311 249 33 value value NOUN bjmsr-311 249 34 . . PUNCT bjmsr-311 250 1 that that PRON bjmsr-311 250 2 is be AUX bjmsr-311 250 3 the the DET bjmsr-311 250 4 previous previous ADJ bjmsr-311 250 5 observation observation NOUN bjmsr-311 250 6 is be AUX bjmsr-311 250 7 again again ADV bjmsr-311 250 8 reached reach VERB bjmsr-311 250 9 , , PUNCT bjmsr-311 250 10 namely namely ADV bjmsr-311 250 11 , , PUNCT bjmsr-311 250 12 sk1a sk1a PROPN bjmsr-311 250 13 * * PUNCT bjmsr-311 250 14 > > X bjmsr-311 250 15 sab sab PROPN bjmsr-311 250 16 * * X bjmsr-311 250 17 > > X bjmsr-311 250 18 sbc sbc PROPN bjmsr-311 250 19 * * PROPN bjmsr-311 250 20 > > X bjmsr-311 250 21 scd scd PROPN bjmsr-311 250 22 * * X bjmsr-311 250 23 > > X bjmsr-311 250 24 ... ... PUNCT bjmsr-311 251 1 > > X bjmsr-311 252 1 sfg sfg PROPN bjmsr-311 252 2 * * PUNCT bjmsr-311 252 3 = = SYM bjmsr-311 252 4 sgf sgf PROPN bjmsr-311 252 5 * * PROPN bjmsr-311 252 6 = = SYM bjmsr-311 252 7 s s X bjmsr-311 252 8 * * PUNCT bjmsr-311 252 9 ( ( PUNCT bjmsr-311 252 10 62 62 NUM bjmsr-311 252 11 ) ) PUNCT bjmsr-311 252 12 the the DET bjmsr-311 252 13 relation relation NOUN bjmsr-311 252 14 ( ( PUNCT bjmsr-311 252 15 62 62 NUM bjmsr-311 252 16 ) ) PUNCT bjmsr-311 252 17 guarantees guarantee VERB bjmsr-311 252 18 that that SCONJ bjmsr-311 252 19 at at ADP bjmsr-311 252 20 each each DET bjmsr-311 252 21 step step NOUN bjmsr-311 252 22 , , PUNCT bjmsr-311 252 23 we we PRON bjmsr-311 252 24 are be AUX bjmsr-311 252 25 descending descend VERB bjmsr-311 252 26 down down ADP bjmsr-311 252 27 the the DET bjmsr-311 252 28 objective objective ADJ bjmsr-311 252 29 function function NOUN bjmsr-311 252 30 surface surface NOUN bjmsr-311 252 31 . . PUNCT bjmsr-311 253 1 4.1 4.1 NUM bjmsr-311 253 2 algorithm algorithm NOUN bjmsr-311 253 3 3 3 NUM bjmsr-311 253 4 to to PART bjmsr-311 253 5 generalize generalize VERB bjmsr-311 253 6 the the DET bjmsr-311 253 7 above above ADJ bjmsr-311 253 8 algorithm algorithm NOUN bjmsr-311 253 9 to to ADP bjmsr-311 253 10 the the DET bjmsr-311 253 11 m m PROPN bjmsr-311 253 12 parameters parameter NOUN bjmsr-311 253 13 linear linear ADJ bjmsr-311 253 14 model model NOUN bjmsr-311 253 15 ( ( PUNCT bjmsr-311 253 16 1 1 NUM bjmsr-311 253 17 ) ) PUNCT bjmsr-311 253 18 , , PUNCT bjmsr-311 253 19 we we PRON bjmsr-311 253 20 should should AUX bjmsr-311 253 21 reduce reduce VERB bjmsr-311 253 22 the the DET bjmsr-311 253 23 number number NOUN bjmsr-311 253 24 of of ADP bjmsr-311 253 25 parameters parameter NOUN bjmsr-311 253 26 in in ADP bjmsr-311 253 27 the the DET bjmsr-311 253 28 same same ADJ bjmsr-311 253 29 fashion fashion NOUN bjmsr-311 253 30 as as ADP bjmsr-311 253 31 in in ADP bjmsr-311 253 32 the the DET bjmsr-311 253 33 case case NOUN bjmsr-311 253 34 of of ADP bjmsr-311 253 35 three three NUM bjmsr-311 253 36 parameters parameter NOUN bjmsr-311 253 37 model model NOUN bjmsr-311 253 38 explained explain VERB bjmsr-311 253 39 above above ADV bjmsr-311 253 40 . . PUNCT bjmsr-311 254 1 if if SCONJ bjmsr-311 254 2 the the DET bjmsr-311 254 3 model model NOUN bjmsr-311 254 4 is be AUX bjmsr-311 254 5 restricted restrict VERB bjmsr-311 254 6 , , PUNCT bjmsr-311 254 7 we we PRON bjmsr-311 254 8 can can AUX bjmsr-311 254 9 make make VERB bjmsr-311 254 10 it it PRON bjmsr-311 254 11 unrestricted unrestricted ADJ bjmsr-311 254 12 by by ADP bjmsr-311 254 13 dividing divide VERB bjmsr-311 254 14 all all PRON bjmsr-311 254 15 dependent dependent ADJ bjmsr-311 254 16 and and CCONJ bjmsr-311 254 17 independent independent ADJ bjmsr-311 254 18 variables variable NOUN bjmsr-311 254 19 to to ADP bjmsr-311 254 20 one one NUM bjmsr-311 254 21 of of ADP bjmsr-311 254 22 the the DET bjmsr-311 254 23 independent independent ADJ bjmsr-311 254 24 variables variable NOUN bjmsr-311 254 25 as as SCONJ bjmsr-311 254 26 follows follow VERB bjmsr-311 254 27 . . PUNCT bjmsr-311 255 1 n n PRON bjmsr-311 255 2 m m VERB bjmsr-311 255 3 n n PRON bjmsr-311 256 1 m m PROPN bjmsr-311 256 2 s s NOUN bjmsr-311 256 3 = = SYM bjmsr-311 256 4 σ σ PROPN bjmsr-311 256 5 │ │ NOUN bjmsr-311 256 6 yiσ yiσ PROPN bjmsr-311 256 7 ßjxji ßjxji VERB bjmsr-311 256 8 │ │ ADJ bjmsr-311 256 9 = = SYM bjmsr-311 256 10 σ σ NOUN bjmsr-311 256 11 │ │ NOUN bjmsr-311 256 12 x2i x2i NUM bjmsr-311 256 13 │ │ VERB bjmsr-311 256 14 │ │ NOUN bjmsr-311 256 15 yi yi NOUN bjmsr-311 256 16 / / SYM bjmsr-311 256 17 x2i x2i PROPN bjmsr-311 256 18 -ß2σ -ß2σ PROPN bjmsr-311 256 19 ßjxji ßjxji PROPN bjmsr-311 256 20 │ │ X bjmsr-311 256 21 ( ( PUNCT bjmsr-311 256 22 63 63 NUM bjmsr-311 256 23 ) ) PUNCT bjmsr-311 256 24 i=1 i=1 PROPN bjmsr-311 257 1 j=2 j=2 X bjmsr-311 257 2 i=1 i=1 X bjmsr-311 258 1 j=3 j=3 X bjmsr-311 258 2 if if SCONJ bjmsr-311 258 3 the the DET bjmsr-311 258 4 model model NOUN bjmsr-311 258 5 is be AUX bjmsr-311 258 6 unrestricted unrestricted ADJ bjmsr-311 258 7 , , PUNCT bjmsr-311 258 8 we we PRON bjmsr-311 258 9 can can AUX bjmsr-311 258 10 make make VERB bjmsr-311 258 11 it it PRON bjmsr-311 258 12 restricted restrict VERB bjmsr-311 258 13 by by ADP bjmsr-311 258 14 deviating deviate VERB bjmsr-311 258 15 all all DET bjmsr-311 258 16 observations observation NOUN bjmsr-311 258 17 from from ADP bjmsr-311 258 18 an an DET bjmsr-311 258 19 arbitrary arbitrary ADJ bjmsr-311 258 20 one one NUM bjmsr-311 258 21 observation observation NOUN bjmsr-311 258 22 ; ; PUNCT bjmsr-311 258 23 namely namely ADV bjmsr-311 258 24 , , PUNCT bjmsr-311 258 25 n n CCONJ bjmsr-311 258 26 m m VERB bjmsr-311 258 27 n n NOUN bjmsr-311 258 28 m m PROPN bjmsr-311 258 29 s s NOUN bjmsr-311 258 30 = = X bjmsr-311 258 31 σ σ PROPN bjmsr-311 258 32 │ │ ADJ bjmsr-311 258 33 yi yi NOUN bjmsr-311 258 34 - - PUNCT bjmsr-311 258 35 ß1σ ß1σ ADJ bjmsr-311 258 36 ßjxji ßjxji NOUN bjmsr-311 258 37 │ │ X bjmsr-311 258 38 = = SYM bjmsr-311 258 39 σ σ PROPN bjmsr-311 258 40 │ │ NOUN bjmsr-311 258 41 yi yi PROPN bjmsr-311 258 42 k1 k1 PROPN bjmsr-311 258 43 σ σ PROPN bjmsr-311 258 44 ßjxji ßjxji PROPN bjmsr-311 258 45 k1 k1 NOUN bjmsr-311 258 46 │ │ X bjmsr-311 258 47 ( ( PUNCT bjmsr-311 258 48 64 64 NUM bjmsr-311 258 49 ) ) PUNCT bjmsr-311 258 50 i=1 i=1 PROPN bjmsr-311 259 1 j=2 j=2 PROPN bjmsr-311 259 2 i=1 i=1 PROPN bjmsr-311 260 1 j=2 j=2 PROPN bjmsr-311 260 2 where where SCONJ bjmsr-311 260 3 , , PUNCT bjmsr-311 260 4 yi yi PROPN bjmsr-311 260 5 k1 k1 PROPN bjmsr-311 260 6 = = SYM bjmsr-311 260 7 yi yi PROPN bjmsr-311 260 8 yk1 yk1 PROPN bjmsr-311 260 9 , , PUNCT bjmsr-311 260 10 xji xji PROPN bjmsr-311 260 11 k1 k1 NOUN bjmsr-311 260 12 = = PUNCT bjmsr-311 260 13 xji xji PROPN bjmsr-311 260 14 xjk1 xjk1 PROPN bjmsr-311 260 15 i=1, i=1, PROPN bjmsr-311 260 16 ... ... PUNCT bjmsr-311 260 17 ,n ,n PROPN bjmsr-311 260 18 ; ; PUNCT bjmsr-311 260 19 j=2, j=2, PROPN bjmsr-311 260 20 ... ... X bjmsr-311 260 21 ,m ,m PUNCT bjmsr-311 260 22 ( ( PUNCT bjmsr-311 260 23 65 65 NUM bjmsr-311 260 24 ) ) PUNCT bjmsr-311 260 25 therefore therefore ADV bjmsr-311 260 26 , , PUNCT bjmsr-311 260 27 according accord VERB bjmsr-311 260 28 to to ADP bjmsr-311 260 29 the the DET bjmsr-311 260 30 transformations transformation NOUN bjmsr-311 260 31 ( ( PUNCT bjmsr-311 260 32 63 63 NUM bjmsr-311 260 33 ) ) PUNCT bjmsr-311 260 34 , , PUNCT bjmsr-311 260 35 ( ( PUNCT bjmsr-311 260 36 64 64 NUM bjmsr-311 260 37 ) ) PUNCT bjmsr-311 260 38 and and CCONJ bjmsr-311 260 39 ( ( PUNCT bjmsr-311 260 40 65 65 NUM bjmsr-311 260 41 ) ) PUNCT bjmsr-311 260 42 , , PUNCT bjmsr-311 260 43 any any DET bjmsr-311 260 44 m m NOUN bjmsr-311 260 45 parameters parameter NOUN bjmsr-311 260 46 model model NOUN bjmsr-311 260 47 can can AUX bjmsr-311 260 48 be be AUX bjmsr-311 260 49 reduced reduce VERB bjmsr-311 260 50 to to ADP bjmsr-311 260 51 a a DET bjmsr-311 260 52 simple simple ADJ bjmsr-311 260 53 restricted restrict VERB bjmsr-311 260 54 one one NUM bjmsr-311 260 55 parameter parameter NOUN bjmsr-311 260 56 model model NOUN bjmsr-311 260 57 and and CCONJ bjmsr-311 260 58 then then ADV bjmsr-311 260 59 be be AUX bjmsr-311 260 60 estimated estimate VERB bjmsr-311 260 61 as as ADP bjmsr-311 260 62 a a DET bjmsr-311 260 63 weighted weight VERB bjmsr-311 260 64 median median ADJ bjmsr-311 260 65 problem problem NOUN bjmsr-311 260 66 . . PUNCT bjmsr-311 261 1 to to PART bjmsr-311 261 2 conduct conduct VERB bjmsr-311 261 3 this this DET bjmsr-311 261 4 transformation transformation NOUN bjmsr-311 261 5 , , PUNCT bjmsr-311 261 6 if if SCONJ bjmsr-311 261 7 the the DET bjmsr-311 261 8 model model NOUN bjmsr-311 261 9 is be AUX bjmsr-311 261 10 unrestricted unrestricted ADJ bjmsr-311 261 11 , , PUNCT bjmsr-311 261 12 we we PRON bjmsr-311 261 13 should should AUX bjmsr-311 261 14 deviate deviate VERB bjmsr-311 261 15 all all DET bjmsr-311 261 16 observations observation NOUN bjmsr-311 261 17 from from ADP bjmsr-311 261 18 an an DET bjmsr-311 261 19 arbitrary arbitrary ADJ bjmsr-311 261 20 one one NOUN bjmsr-311 261 21 and and CCONJ bjmsr-311 261 22 make make VERB bjmsr-311 261 23 the the DET bjmsr-311 261 24 model model NOUN bjmsr-311 261 25 restricted restrict VERB bjmsr-311 261 26 . . PUNCT bjmsr-311 262 1 then then ADV bjmsr-311 262 2 divide divide VERB bjmsr-311 262 3 all all PRON bjmsr-311 262 4 dependent dependent ADJ bjmsr-311 262 5 and and CCONJ bjmsr-311 262 6 independent independent ADJ bjmsr-311 262 7 variables variable NOUN bjmsr-311 262 8 to to ADP bjmsr-311 262 9 an an DET bjmsr-311 262 10 arbitrary arbitrary ADJ bjmsr-311 262 11 independent independent ADJ bjmsr-311 262 12 variable variable NOUN bjmsr-311 262 13 . . PUNCT bjmsr-311 263 1 this this PRON bjmsr-311 263 2 makes make VERB bjmsr-311 263 3 the the DET bjmsr-311 263 4 model model NOUN bjmsr-311 263 5 unrestricted unrestricted ADJ bjmsr-311 263 6 . . PUNCT bjmsr-311 264 1 at at ADP bjmsr-311 264 2 this this DET bjmsr-311 264 3 step step NOUN bjmsr-311 264 4 , , PUNCT bjmsr-311 264 5 we we PRON bjmsr-311 264 6 have have AUX bjmsr-311 264 7 reduced reduce VERB bjmsr-311 264 8 the the DET bjmsr-311 264 9 number number NOUN bjmsr-311 264 10 of of ADP bjmsr-311 264 11 parameters parameter NOUN bjmsr-311 264 12 by by ADP bjmsr-311 264 13 one one NUM bjmsr-311 264 14 . . PUNCT bjmsr-311 265 1 by by ADP bjmsr-311 265 2 continuing continue VERB bjmsr-311 265 3 this this DET bjmsr-311 265 4 process process NOUN bjmsr-311 265 5 , , PUNCT bjmsr-311 265 6 we we PRON bjmsr-311 265 7 can can AUX bjmsr-311 265 8 reduce reduce VERB bjmsr-311 265 9 any any DET bjmsr-311 265 10 m m NOUN bjmsr-311 265 11 parameters parameter NOUN bjmsr-311 265 12 model model NOUN bjmsr-311 265 13 to to ADP bjmsr-311 265 14 a a DET bjmsr-311 265 15 oneparameter oneparameter ADJ bjmsr-311 265 16 model model NOUN bjmsr-311 265 17 . . PUNCT bjmsr-311 266 1 if if SCONJ bjmsr-311 266 2 the the DET bjmsr-311 266 3 model model NOUN bjmsr-311 266 4 is be AUX bjmsr-311 266 5 restricted restrict VERB bjmsr-311 266 6 , , PUNCT bjmsr-311 266 7 we we PRON bjmsr-311 266 8 should should AUX bjmsr-311 266 9 start start VERB bjmsr-311 266 10 by by ADP bjmsr-311 266 11 dividing divide VERB bjmsr-311 266 12 all all PRON bjmsr-311 266 13 of of ADP bjmsr-311 266 14 the the DET bjmsr-311 266 15 variables variable NOUN bjmsr-311 266 16 by by ADP bjmsr-311 266 17 one one NUM bjmsr-311 266 18 of of ADP bjmsr-311 266 19 the the DET bjmsr-311 266 20 independent independent ADJ bjmsr-311 266 21 variables variable NOUN bjmsr-311 266 22 and and CCONJ bjmsr-311 266 23 make make VERB bjmsr-311 266 24 the the DET bjmsr-311 266 25 model model NOUN bjmsr-311 266 26 unrestricted unrestricted ADJ bjmsr-311 266 27 . . PUNCT bjmsr-311 267 1 now now ADV bjmsr-311 267 2 , , PUNCT bjmsr-311 267 3 we we PRON bjmsr-311 267 4 can can AUX bjmsr-311 267 5 again again ADV bjmsr-311 267 6 reduce reduce VERB bjmsr-311 267 7 one one NUM bjmsr-311 267 8 of of ADP bjmsr-311 267 9 the the DET bjmsr-311 267 10 parameters parameter NOUN bjmsr-311 267 11 by by ADP bjmsr-311 267 12 applying apply VERB bjmsr-311 267 13 the the DET bjmsr-311 267 14 procedures procedure NOUN bjmsr-311 267 15 explained explain VERB bjmsr-311 267 16 above above ADV bjmsr-311 267 17 in in ADP bjmsr-311 267 18 order order NOUN bjmsr-311 267 19 to to PART bjmsr-311 267 20 transform transform VERB bjmsr-311 267 21 the the DET bjmsr-311 267 22 unrestricted unrestricted ADJ bjmsr-311 267 23 model model NOUN bjmsr-311 267 24 to to ADP bjmsr-311 267 25 restricted restricted ADJ bjmsr-311 267 26 form form NOUN bjmsr-311 267 27 . . PUNCT bjmsr-311 268 1 by by ADP bjmsr-311 268 2 solving solve VERB bjmsr-311 268 3 the the DET bjmsr-311 268 4 one one NUM bjmsr-311 268 5 parameter parameter NOUN bjmsr-311 268 6 model model NOUN bjmsr-311 268 7 , , PUNCT bjmsr-311 268 8 we we PRON bjmsr-311 268 9 can can AUX bjmsr-311 268 10 then then ADV bjmsr-311 268 11 solve solve VERB bjmsr-311 268 12 for for ADP bjmsr-311 268 13 the the DET bjmsr-311 268 14 two two NUM bjmsr-311 268 15 parameters parameter NOUN bjmsr-311 268 16 and and CCONJ bjmsr-311 268 17 then then ADV bjmsr-311 268 18 three three NUM bjmsr-311 268 19 parameters parameter NOUN bjmsr-311 268 20 models model NOUN bjmsr-311 268 21 and and CCONJ bjmsr-311 268 22 so so ADV bjmsr-311 268 23 on on ADV bjmsr-311 268 24 . . PUNCT bjmsr-311 269 1 the the DET bjmsr-311 269 2 most most ADV bjmsr-311 269 3 delicate delicate ADJ bjmsr-311 269 4 part part NOUN bjmsr-311 269 5 of of ADP bjmsr-311 269 6 this this DET bjmsr-311 269 7 algorithm algorithm NOUN bjmsr-311 269 8 is be AUX bjmsr-311 269 9 that that SCONJ bjmsr-311 269 10 , , PUNCT bjmsr-311 269 11 at at ADP bjmsr-311 269 12 the the DET bjmsr-311 269 13 starting starting NOUN bjmsr-311 269 14 point point NOUN bjmsr-311 269 15 , , PUNCT bjmsr-311 269 16 once once SCONJ bjmsr-311 269 17 k1,k2, k1,k2, PROPN bjmsr-311 269 18 ... ... PUNCT bjmsr-311 269 19 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 269 20 ) ) PUNCT bjmsr-311 269 21 are be AUX bjmsr-311 269 22 selected select VERB bjmsr-311 269 23 arbitrarily arbitrarily ADV bjmsr-311 269 24 , , PUNCT bjmsr-311 269 25 then then ADV bjmsr-311 269 26 the the DET bjmsr-311 269 27 algorithm algorithm NOUN bjmsr-311 269 28 assigns assign VERB bjmsr-311 269 29 the the DET bjmsr-311 269 30 best well ADV bjmsr-311 269 31 possible possible ADJ bjmsr-311 269 32 values value NOUN bjmsr-311 269 33 to to ADP bjmsr-311 269 34 the the DET bjmsr-311 269 35 integers integer NOUN bjmsr-311 269 36 k1,k2, k1,k2, ADJ bjmsr-311 269 37 ... ... PUNCT bjmsr-311 269 38 ,k(m-1 ,k(m-1 PROPN bjmsr-311 269 39 ) ) PUNCT bjmsr-311 269 40 . . PUNCT bjmsr-311 270 1 to to PART bjmsr-311 270 2 explain explain VERB bjmsr-311 270 3 the the DET bjmsr-311 270 4 procedure procedure NOUN bjmsr-311 270 5 , , PUNCT bjmsr-311 270 6 let let VERB bjmsr-311 270 7 us we PRON bjmsr-311 270 8 deal deal VERB bjmsr-311 270 9 with with ADP bjmsr-311 270 10 the the DET bjmsr-311 270 11 four four NUM bjmsr-311 270 12 parameters parameter NOUN bjmsr-311 270 13 unrestricted unrestricted ADJ bjmsr-311 270 14 linear linear PROPN bjmsr-311 270 15 model model NOUN bjmsr-311 270 16 . . PUNCT bjmsr-311 271 1 once once ADV bjmsr-311 271 2 , , PUNCT bjmsr-311 271 3 the the DET bjmsr-311 271 4 value value NOUN bjmsr-311 271 5 of of ADP bjmsr-311 271 6 k1 k1 NOUN bjmsr-311 271 7 is be AUX bjmsr-311 271 8 arbitrarily arbitrarily ADV bjmsr-311 271 9 selected select VERB bjmsr-311 271 10 . . PUNCT bjmsr-311 272 1 deviate deviate VERB bjmsr-311 272 2 all all DET bjmsr-311 272 3 observations observation NOUN bjmsr-311 272 4 from from ADP bjmsr-311 272 5 k1 k1 PROPN bjmsr-311 272 6 th th NUM bjmsr-311 272 7 observation observation NOUN bjmsr-311 272 8 . . PUNCT bjmsr-311 273 1 in in ADP bjmsr-311 273 2 this this DET bjmsr-311 273 3 way way NOUN bjmsr-311 273 4 , , PUNCT bjmsr-311 273 5 the the DET bjmsr-311 273 6 model model NOUN bjmsr-311 273 7 reduces reduce VERB bjmsr-311 273 8 to to ADP bjmsr-311 273 9 a a DET bjmsr-311 273 10 three three NUM bjmsr-311 273 11 parameters parameter NOUN bjmsr-311 273 12 restricted restrict VERB bjmsr-311 273 13 model model NOUN bjmsr-311 273 14 . . PUNCT bjmsr-311 274 1 by by ADP bjmsr-311 274 2 dividing divide VERB bjmsr-311 274 3 all all PRON bjmsr-311 274 4 of of ADP bjmsr-311 274 5 the the DET bjmsr-311 274 6 variables variable NOUN bjmsr-311 274 7 to to ADP bjmsr-311 274 8 one one NUM bjmsr-311 274 9 of of ADP bjmsr-311 274 10 the the DET bjmsr-311 274 11 independent independent ADJ bjmsr-311 274 12 variables variable NOUN bjmsr-311 274 13 , , PUNCT bjmsr-311 274 14 our our PRON bjmsr-311 274 15 model model NOUN bjmsr-311 274 16 becomes become VERB bjmsr-311 274 17 completely completely ADV bjmsr-311 274 18 similar similar ADJ bjmsr-311 274 19 to to ADP bjmsr-311 274 20 ( ( PUNCT bjmsr-311 274 21 44 44 NUM bjmsr-311 274 22 ) ) PUNCT bjmsr-311 274 23 . . PUNCT bjmsr-311 275 1 by by ADP bjmsr-311 275 2 minimizing minimize VERB bjmsr-311 275 3 ( ( PUNCT bjmsr-311 275 4 44 44 NUM bjmsr-311 275 5 ) ) PUNCT bjmsr-311 275 6 according accord VERB bjmsr-311 275 7 to to ADP bjmsr-311 275 8 the the DET bjmsr-311 275 9 algorithm algorithm NOUN bjmsr-311 275 10 previously previously ADV bjmsr-311 275 11 explained explain VERB bjmsr-311 275 12 for for ADP bjmsr-311 275 13 the the DET bjmsr-311 275 14 three three NUM bjmsr-311 275 15 parameters parameter NOUN bjmsr-311 275 16 model model NOUN bjmsr-311 275 17 , , PUNCT bjmsr-311 275 18 subscript subscript PROPN bjmsr-311 275 19 m m PROPN bjmsr-311 275 20 corresponding correspond VERB bjmsr-311 275 21 to to PART bjmsr-311 275 22 mth mth NOUN bjmsr-311 275 23 point point NOUN bjmsr-311 275 24 is be AUX bjmsr-311 275 25 derived derive VERB bjmsr-311 275 26 . . PUNCT bjmsr-311 276 1 this this PRON bjmsr-311 276 2 is be AUX bjmsr-311 276 3 the the DET bjmsr-311 276 4 newly newly ADV bjmsr-311 276 5 found find VERB bjmsr-311 276 6 point point NOUN bjmsr-311 276 7 which which PRON bjmsr-311 276 8 its its PRON bjmsr-311 276 9 subscript subscript NOUN bjmsr-311 276 10 ( ( PUNCT bjmsr-311 276 11 m m NOUN bjmsr-311 276 12 ) ) PUNCT bjmsr-311 276 13 is be AUX bjmsr-311 276 14 assigned assign VERB bjmsr-311 276 15 to to ADP bjmsr-311 276 16 k1 k1 PROPN bjmsr-311 276 17 . . PUNCT bjmsr-311 277 1 the the DET bjmsr-311 277 2 previous previous ADJ bjmsr-311 277 3 value value NOUN bjmsr-311 277 4 of of ADP bjmsr-311 277 5 k1 k1 NOUN bjmsr-311 277 6 is be AUX bjmsr-311 277 7 assigned assign VERB bjmsr-311 277 8 to to ADP bjmsr-311 277 9 k2 k2 NOUN bjmsr-311 277 10 , , PUNCT bjmsr-311 277 11 and and CCONJ bjmsr-311 277 12 the the DET bjmsr-311 277 13 previous previous ADJ bjmsr-311 277 14 value value NOUN bjmsr-311 277 15 of of ADP bjmsr-311 277 16 k2 k2 PROPN bjmsr-311 277 17 is be AUX bjmsr-311 277 18 assigned assign VERB bjmsr-311 277 19 to to PART bjmsr-311 277 20 k3 k3 VERB bjmsr-311 277 21 , , PUNCT bjmsr-311 277 22 and and CCONJ bjmsr-311 277 23 the the DET bjmsr-311 277 24 whole whole ADJ bjmsr-311 277 25 procedure procedure NOUN bjmsr-311 277 26 is be AUX bjmsr-311 277 27 repeated repeat VERB bjmsr-311 277 28 again again ADV bjmsr-311 277 29 . . PUNCT bjmsr-311 278 1 the the DET bjmsr-311 278 2 procedure procedure NOUN bjmsr-311 278 3 stops stop VERB bjmsr-311 278 4 when when SCONJ bjmsr-311 278 5 the the DET bjmsr-311 278 6 value value NOUN bjmsr-311 278 7 of of ADP bjmsr-311 278 8 m m NOUN bjmsr-311 278 9 is be AUX bjmsr-311 278 10 equal equal ADJ bjmsr-311 278 11 to to ADP bjmsr-311 278 12 k1 k1 PROPN bjmsr-311 278 13 . . PUNCT bjmsr-311 279 1 the the DET bjmsr-311 279 2 above above ADJ bjmsr-311 279 3 important important ADJ bjmsr-311 279 4 assigning assign VERB bjmsr-311 279 5 technique technique NOUN bjmsr-311 279 6 , , PUNCT bjmsr-311 279 7 which which PRON bjmsr-311 279 8 is be AUX bjmsr-311 279 9 essential essential ADJ bjmsr-311 279 10 for for ADP bjmsr-311 279 11 pivoting pivot VERB bjmsr-311 279 12 on on ADP bjmsr-311 279 13 the the DET bjmsr-311 279 14 origins origin NOUN bjmsr-311 279 15 of of ADP bjmsr-311 279 16 different different ADJ bjmsr-311 279 17 size size NOUN bjmsr-311 279 18 coordinates coordinate NOUN bjmsr-311 279 19 , , PUNCT bjmsr-311 279 20 can can AUX bjmsr-311 279 21 be be AUX bjmsr-311 279 22 extended extend VERB bjmsr-311 279 23 to to ADP bjmsr-311 279 24 more more ADJ bjmsr-311 279 25 parameters parameter NOUN bjmsr-311 279 26 models model NOUN bjmsr-311 279 27 as as SCONJ bjmsr-311 279 28 we we PRON bjmsr-311 279 29 did do VERB bjmsr-311 279 30 before before ADV bjmsr-311 279 31 . . PUNCT bjmsr-311 280 1 again again ADV bjmsr-311 280 2 , , PUNCT bjmsr-311 280 3 we we PRON bjmsr-311 280 4 should should AUX bjmsr-311 280 5 note note VERB bjmsr-311 280 6 that that SCONJ bjmsr-311 280 7 at at ADP bjmsr-311 280 8 each each DET bjmsr-311 280 9 succeeding succeed VERB bjmsr-311 280 10 step step NOUN bjmsr-311 280 11 , , PUNCT bjmsr-311 280 12 we we PRON bjmsr-311 280 13 get get VERB bjmsr-311 280 14 closer close ADJ bjmsr-311 280 15 to to ADP bjmsr-311 280 16 the the DET bjmsr-311 280 17 minimum minimum NOUN bjmsr-311 280 18 of of ADP bjmsr-311 280 19 s s PRON bjmsr-311 280 20 in in ADP bjmsr-311 280 21 ( ( PUNCT bjmsr-311 280 22 1 1 NUM bjmsr-311 280 23 ) ) PUNCT bjmsr-311 280 24 . . PUNCT bjmsr-311 281 1 the the DET bjmsr-311 281 2 proof proof NOUN bjmsr-311 281 3 is be AUX bjmsr-311 281 4 completely completely ADV bjmsr-311 281 5 similar similar ADJ bjmsr-311 281 6 to to ADP bjmsr-311 281 7 the the DET bjmsr-311 281 8 three three NUM bjmsr-311 281 9 parameters parameter NOUN bjmsr-311 281 10 model model NOUN bjmsr-311 281 11 explained explain VERB bjmsr-311 281 12 before before ADV bjmsr-311 281 13 . . PUNCT bjmsr-311 282 1 the the DET bjmsr-311 282 2 whole whole ADJ bjmsr-311 282 3 procedure procedure NOUN bjmsr-311 282 4 is be AUX bjmsr-311 282 5 as as SCONJ bjmsr-311 282 6 follows follow VERB bjmsr-311 282 7 . . PUNCT bjmsr-311 283 1 algorithm algorithm NOUN bjmsr-311 283 2 3 3 NUM bjmsr-311 283 3 step step NOUN bjmsr-311 283 4 0 0 NUM bjmsr-311 283 5 ) ) PUNCT bjmsr-311 283 6 select select ADJ bjmsr-311 283 7 arbitrary arbitrary ADJ bjmsr-311 283 8 points point NOUN bjmsr-311 283 9 k1,k2, k1,k2, NOUN bjmsr-311 283 10 ... ... PUNCT bjmsr-311 283 11 ,k(m-1 ,k(m-1 PROPN bjmsr-311 283 12 ) ) PUNCT bjmsr-311 283 13 . . PUNCT bjmsr-311 284 1 step step NOUN bjmsr-311 284 2 1 1 NUM bjmsr-311 284 3 ) ) PUNCT bjmsr-311 284 4 set set NOUN bjmsr-311 284 5 counter=1 counter=1 PROPN bjmsr-311 284 6 . . PUNCT bjmsr-311 285 1 step step NOUN bjmsr-311 285 2 2 2 NUM bjmsr-311 285 3 ) ) PUNCT bjmsr-311 285 4 proceed proceed VERB bjmsr-311 285 5 the the DET bjmsr-311 285 6 transformations transformation NOUN bjmsr-311 285 7 ( ( PUNCT bjmsr-311 285 8 63 63 NUM bjmsr-311 285 9 ) ) PUNCT bjmsr-311 285 10 through through ADP bjmsr-311 285 11 ( ( PUNCT bjmsr-311 285 12 65 65 NUM bjmsr-311 285 13 ) ) PUNCT bjmsr-311 285 14 to to PART bjmsr-311 285 15 reduce reduce VERB bjmsr-311 285 16 the the DET bjmsr-311 285 17 model model NOUN bjmsr-311 285 18 to to ADP bjmsr-311 285 19 a a DET bjmsr-311 285 20 one one NUM bjmsr-311 285 21 - - PUNCT bjmsr-311 285 22 parameter parameter NOUN bjmsr-311 285 23 transformed transform VERB bjmsr-311 285 24 restricted restrict VERB bjmsr-311 285 25 linear linear NOUN bjmsr-311 285 26 model model NOUN bjmsr-311 285 27 . . PUNCT bjmsr-311 286 1 step step NOUN bjmsr-311 286 2 3 3 NUM bjmsr-311 286 3 ) ) PUNCT bjmsr-311 286 4 apply apply VERB bjmsr-311 286 5 weighted weight VERB bjmsr-311 286 6 median median ADJ bjmsr-311 286 7 procedure procedure NOUN bjmsr-311 286 8 to to PART bjmsr-311 286 9 find find VERB bjmsr-311 286 10 the the DET bjmsr-311 286 11 point point NOUN bjmsr-311 286 12 m. m. NOUN bjmsr-311 286 13 step step NOUN bjmsr-311 286 14 4 4 NUM bjmsr-311 286 15 ) ) PUNCT bjmsr-311 286 16 if if SCONJ bjmsr-311 286 17 m m NOUN bjmsr-311 286 18 is be AUX bjmsr-311 286 19 equal equal ADJ bjmsr-311 286 20 to to ADP bjmsr-311 286 21 the the DET bjmsr-311 286 22 previous previous ADJ bjmsr-311 286 23 value value NOUN bjmsr-311 286 24 of of ADP bjmsr-311 286 25 k(counter k(counter NOUN bjmsr-311 286 26 ) ) PUNCT bjmsr-311 286 27 go go VERB bjmsr-311 286 28 to to PART bjmsr-311 286 29 step step VERB bjmsr-311 286 30 5 5 NUM bjmsr-311 286 31 ; ; PUNCT bjmsr-311 286 32 otherwise otherwise ADV bjmsr-311 286 33 set set VERB bjmsr-311 286 34 k(counter)=m k(counter)=m NOUN bjmsr-311 286 35 and and CCONJ bjmsr-311 286 36 go go VERB bjmsr-311 286 37 to to PART bjmsr-311 286 38 step step VERB bjmsr-311 286 39 1 1 NUM bjmsr-311 286 40 . . PUNCT bjmsr-311 287 1 step step NOUN bjmsr-311 287 2 5 5 NUM bjmsr-311 287 3 ) ) PUNCT bjmsr-311 287 4 if if SCONJ bjmsr-311 287 5 counter counter NOUN bjmsr-311 287 6 = = SYM bjmsr-311 287 7 m-1 m-1 NUM bjmsr-311 287 8 go go VERB bjmsr-311 287 9 to to PART bjmsr-311 287 10 step step VERB bjmsr-311 287 11 6 6 NUM bjmsr-311 287 12 ; ; PUNCT bjmsr-311 287 13 otherwise otherwise ADV bjmsr-311 287 14 let let VERB bjmsr-311 287 15 counter counter NOUN bjmsr-311 287 16 = = VERB bjmsr-311 287 17 counter+1 counter+1 ADJ bjmsr-311 287 18 and and CCONJ bjmsr-311 287 19 go go VERB bjmsr-311 287 20 to to PART bjmsr-311 287 21 step step VERB bjmsr-311 287 22 4 4 NUM bjmsr-311 287 23 . . PUNCT bjmsr-311 287 24 step step NOUN bjmsr-311 287 25 6 6 NUM bjmsr-311 287 26 ) ) PUNCT bjmsr-311 287 27 set set VERB bjmsr-311 287 28 k(m)=m k(m)=m NOUN bjmsr-311 287 29 . . PUNCT bjmsr-311 287 30 by by ADP bjmsr-311 287 31 using use VERB bjmsr-311 287 32 the the DET bjmsr-311 287 33 final final ADJ bjmsr-311 287 34 values value NOUN bjmsr-311 287 35 of of ADP bjmsr-311 287 36 k1, k1, NOUN bjmsr-311 287 37 ... ... PUNCT bjmsr-311 287 38 ,k(m ,k(m PUNCT bjmsr-311 287 39 ) ) PUNCT bjmsr-311 287 40 solve solve VERB bjmsr-311 287 41 the the DET bjmsr-311 287 42 following follow VERB bjmsr-311 287 43 system system NOUN bjmsr-311 287 44 of of ADP bjmsr-311 287 45 equations equation NOUN bjmsr-311 287 46 for for ADP bjmsr-311 287 47 ß ß DET bjmsr-311 287 48 j^ j^ NOUN bjmsr-311 287 49 , , PUNCT bjmsr-311 287 50 for for ADP bjmsr-311 287 51 j=1, j=1, NOUN bjmsr-311 287 52 ... ... PUNCT bjmsr-311 287 53 ,m ,m PUNCT bjmsr-311 287 54 ; ; PUNCT bjmsr-311 288 1 m m PROPN bjmsr-311 288 2 σ σ NUM bjmsr-311 288 3 ßj^xjki ßj^xjki PROPN bjmsr-311 288 4 = = SYM bjmsr-311 288 5 yki yki NOUN bjmsr-311 288 6 i=1, i=1, NOUN bjmsr-311 288 7 ... ... PUNCT bjmsr-311 288 8 ,m ,m PUNCT bjmsr-311 288 9 j=1 j=1 PROPN bjmsr-311 288 10 stop stop NOUN bjmsr-311 288 11 . . PUNCT bjmsr-311 289 1 copyright copyright NOUN bjmsr-311 289 2 © © PROPN bjmsr-311 289 3 cc cc PROPN bjmsr-311 289 4 - - PUNCT bjmsr-311 289 5 by by ADP bjmsr-311 289 6 - - PUNCT bjmsr-311 289 7 nc nc PROPN bjmsr-311 289 8 2019 2019 NUM bjmsr-311 289 9 , , PUNCT bjmsr-311 289 10 bjmsr bjmsr PROPN bjmsr-311 289 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 290 1 bangladesh bangladesh PROPN bjmsr-311 290 2 journal journal PROPN bjmsr-311 290 3 of of ADP bjmsr-311 290 4 multidisciplinary multidisciplinary ADJ bjmsr-311 290 5 scientific scientific ADJ bjmsr-311 290 6 research research NOUN bjmsr-311 290 7 vol vol NOUN bjmsr-311 290 8 . . PROPN bjmsr-311 290 9 1 1 NUM bjmsr-311 290 10 , , PUNCT bjmsr-311 290 11 no no INTJ bjmsr-311 290 12 . . NOUN bjmsr-311 290 13 1 1 NUM bjmsr-311 290 14 ; ; PUNCT bjmsr-311 290 15 2019 2019 NUM bjmsr-311 290 16 11 11 NUM bjmsr-311 290 17 4.2 4.2 NUM bjmsr-311 290 18 algorithm algorithm NOUN bjmsr-311 290 19 4 4 NUM bjmsr-311 290 20 in in ADP bjmsr-311 290 21 algorithm algorithm NOUN bjmsr-311 290 22 3 3 NUM bjmsr-311 290 23 to to PART bjmsr-311 290 24 solve solve VERB bjmsr-311 290 25 any any DET bjmsr-311 290 26 m m NOUN bjmsr-311 290 27 parameters parameter NOUN bjmsr-311 290 28 model model NOUN bjmsr-311 290 29 , , PUNCT bjmsr-311 290 30 the the DET bjmsr-311 290 31 reduced reduce VERB bjmsr-311 290 32 m-1 m-1 PROPN bjmsr-311 290 33 parameters parameter NOUN bjmsr-311 290 34 model model NOUN bjmsr-311 290 35 should should AUX bjmsr-311 290 36 be be AUX bjmsr-311 290 37 solved solve VERB bjmsr-311 290 38 first first ADV bjmsr-311 290 39 and and CCONJ bjmsr-311 290 40 therefore therefore ADV bjmsr-311 290 41 makes make VERB bjmsr-311 290 42 the the DET bjmsr-311 290 43 algorithm algorithm NOUN bjmsr-311 290 44 rather rather ADV bjmsr-311 290 45 costly costly ADJ bjmsr-311 290 46 . . PUNCT bjmsr-311 291 1 because because SCONJ bjmsr-311 291 2 to to PART bjmsr-311 291 3 solve solve VERB bjmsr-311 291 4 a a DET bjmsr-311 291 5 m m NOUN bjmsr-311 291 6 parameters parameter NOUN bjmsr-311 291 7 model model NOUN bjmsr-311 291 8 , , PUNCT bjmsr-311 291 9 we we PRON bjmsr-311 291 10 should should AUX bjmsr-311 291 11 reduce reduce VERB bjmsr-311 291 12 the the DET bjmsr-311 291 13 objective objective ADJ bjmsr-311 291 14 function function NOUN bjmsr-311 291 15 value value NOUN bjmsr-311 291 16 of of ADP bjmsr-311 291 17 the the DET bjmsr-311 291 18 reduced reduce VERB bjmsr-311 291 19 m-1 m-1 PROPN bjmsr-311 291 20 parameters parameter NOUN bjmsr-311 291 21 model model VERB bjmsr-311 291 22 down down ADP bjmsr-311 291 23 to to ADP bjmsr-311 291 24 its its PRON bjmsr-311 291 25 minimum minimum ADJ bjmsr-311 291 26 value value NOUN bjmsr-311 291 27 and and CCONJ bjmsr-311 291 28 then then ADV bjmsr-311 291 29 going go VERB bjmsr-311 291 30 back back ADV bjmsr-311 291 31 to to ADP bjmsr-311 291 32 the the DET bjmsr-311 291 33 m m PROPN bjmsr-311 291 34 parameters parameter NOUN bjmsr-311 291 35 model model NOUN bjmsr-311 291 36 . . PUNCT bjmsr-311 292 1 in in ADP bjmsr-311 292 2 interior interior ADJ bjmsr-311 292 3 steps step NOUN bjmsr-311 292 4 for for ADP bjmsr-311 292 5 m-1,m-2, m-1,m-2, NOUN bjmsr-311 292 6 ... ... PUNCT bjmsr-311 292 7 ,1 ,1 PUNCT bjmsr-311 292 8 this this DET bjmsr-311 292 9 procedure procedure NOUN bjmsr-311 292 10 repeats repeat VERB bjmsr-311 292 11 . . PUNCT bjmsr-311 293 1 in in ADP bjmsr-311 293 2 order order NOUN bjmsr-311 293 3 to to PART bjmsr-311 293 4 make make VERB bjmsr-311 293 5 this this DET bjmsr-311 293 6 algorithm algorithm NOUN bjmsr-311 293 7 more more ADV bjmsr-311 293 8 efficient efficient ADJ bjmsr-311 293 9 , , PUNCT bjmsr-311 293 10 another another DET bjmsr-311 293 11 assigning assign VERB bjmsr-311 293 12 technique technique NOUN bjmsr-311 293 13 may may AUX bjmsr-311 293 14 be be AUX bjmsr-311 293 15 adopted adopt VERB bjmsr-311 293 16 . . PUNCT bjmsr-311 294 1 once once SCONJ bjmsr-311 294 2 m-1 m-1 PROPN bjmsr-311 294 3 observations observation NOUN bjmsr-311 294 4 are be AUX bjmsr-311 294 5 selected select VERB bjmsr-311 294 6 arbitrarily arbitrarily ADV bjmsr-311 294 7 . . PUNCT bjmsr-311 295 1 the the DET bjmsr-311 295 2 s s NOUN bjmsr-311 295 3 function function NOUN bjmsr-311 295 4 is be AUX bjmsr-311 295 5 reduced reduce VERB bjmsr-311 295 6 to to ADP bjmsr-311 295 7 a a DET bjmsr-311 295 8 one one NUM bjmsr-311 295 9 - - PUNCT bjmsr-311 295 10 parameter parameter NOUN bjmsr-311 295 11 weighted weight VERB bjmsr-311 295 12 median median ADJ bjmsr-311 295 13 problem problem NOUN bjmsr-311 295 14 as as SCONJ bjmsr-311 295 15 we we PRON bjmsr-311 295 16 did do AUX bjmsr-311 295 17 in in ADP bjmsr-311 295 18 algorithm algorithm NOUN bjmsr-311 295 19 3 3 NUM bjmsr-311 295 20 using use VERB bjmsr-311 295 21 ( ( PUNCT bjmsr-311 295 22 63 63 NUM bjmsr-311 295 23 ) ) PUNCT bjmsr-311 295 24 and and CCONJ bjmsr-311 295 25 ( ( PUNCT bjmsr-311 295 26 64 64 NUM bjmsr-311 295 27 ) ) PUNCT bjmsr-311 295 28 . . PUNCT bjmsr-311 296 1 by by ADP bjmsr-311 296 2 solving solve VERB bjmsr-311 296 3 the the DET bjmsr-311 296 4 weighted weight VERB bjmsr-311 296 5 median median ADJ bjmsr-311 296 6 problem problem NOUN bjmsr-311 296 7 , , PUNCT bjmsr-311 296 8 a a DET bjmsr-311 296 9 new new ADJ bjmsr-311 296 10 observation observation NOUN bjmsr-311 296 11 m m VERB bjmsr-311 296 12 is be AUX bjmsr-311 296 13 found find VERB bjmsr-311 296 14 . . PUNCT bjmsr-311 297 1 now now ADV bjmsr-311 297 2 , , PUNCT bjmsr-311 297 3 the the DET bjmsr-311 297 4 newly newly ADV bjmsr-311 297 5 found find VERB bjmsr-311 297 6 point point NOUN bjmsr-311 297 7 is be AUX bjmsr-311 297 8 replaced replace VERB bjmsr-311 297 9 by by ADP bjmsr-311 297 10 the the DET bjmsr-311 297 11 most most ADV bjmsr-311 297 12 previous previous ADJ bjmsr-311 297 13 observation observation NOUN bjmsr-311 297 14 which which PRON bjmsr-311 297 15 entered enter VERB bjmsr-311 297 16 the the DET bjmsr-311 297 17 basis basis NOUN bjmsr-311 297 18 . . PUNCT bjmsr-311 298 1 the the DET bjmsr-311 298 2 procedure procedure NOUN bjmsr-311 298 3 is be AUX bjmsr-311 298 4 repeated repeat VERB bjmsr-311 298 5 until until SCONJ bjmsr-311 298 6 we we PRON bjmsr-311 298 7 can can AUX bjmsr-311 298 8 not not PART bjmsr-311 298 9 find find VERB bjmsr-311 298 10 any any DET bjmsr-311 298 11 new new ADJ bjmsr-311 298 12 observation observation NOUN bjmsr-311 298 13 out out ADP bjmsr-311 298 14 of of ADP bjmsr-311 298 15 the the DET bjmsr-311 298 16 current current ADJ bjmsr-311 298 17 set set NOUN bjmsr-311 298 18 of of ADP bjmsr-311 298 19 basis basis NOUN bjmsr-311 298 20 points point NOUN bjmsr-311 298 21 and and CCONJ bjmsr-311 298 22 the the DET bjmsr-311 298 23 deleted delete VERB bjmsr-311 298 24 point point NOUN bjmsr-311 298 25 in in ADP bjmsr-311 298 26 the the DET bjmsr-311 298 27 previous previous ADJ bjmsr-311 298 28 iteration iteration NOUN bjmsr-311 298 29 . . PUNCT bjmsr-311 299 1 on on ADP bjmsr-311 299 2 the the DET bjmsr-311 299 3 other other ADJ bjmsr-311 299 4 hand hand NOUN bjmsr-311 299 5 , , PUNCT bjmsr-311 299 6 in in ADP bjmsr-311 299 7 this this DET bjmsr-311 299 8 algorithm algorithm NOUN bjmsr-311 299 9 m-1 m-1 PROPN bjmsr-311 299 10 point point NOUN bjmsr-311 299 11 is be AUX bjmsr-311 299 12 selected select VERB bjmsr-311 299 13 as as ADP bjmsr-311 299 14 a a DET bjmsr-311 299 15 basic basic ADJ bjmsr-311 299 16 feasible feasible ADJ bjmsr-311 299 17 solution solution NOUN bjmsr-311 299 18 . . PUNCT bjmsr-311 300 1 by by ADP bjmsr-311 300 2 pivoting pivot VERB bjmsr-311 300 3 on on ADP bjmsr-311 300 4 this this DET bjmsr-311 300 5 solution solution NOUN bjmsr-311 300 6 , , PUNCT bjmsr-311 300 7 a a DET bjmsr-311 300 8 new new ADJ bjmsr-311 300 9 point point NOUN bjmsr-311 300 10 is be AUX bjmsr-311 300 11 found find VERB bjmsr-311 300 12 to to PART bjmsr-311 300 13 enter enter VERB bjmsr-311 300 14 the the DET bjmsr-311 300 15 basis basis NOUN bjmsr-311 300 16 and and CCONJ bjmsr-311 300 17 should should AUX bjmsr-311 300 18 be be AUX bjmsr-311 300 19 replaced replace VERB bjmsr-311 300 20 by by ADP bjmsr-311 300 21 another another DET bjmsr-311 300 22 one one NOUN bjmsr-311 300 23 which which PRON bjmsr-311 300 24 was be AUX bjmsr-311 300 25 previously previously ADV bjmsr-311 300 26 on on ADP bjmsr-311 300 27 the the DET bjmsr-311 300 28 basis basis NOUN bjmsr-311 300 29 . . PUNCT bjmsr-311 301 1 the the DET bjmsr-311 301 2 procedure procedure NOUN bjmsr-311 301 3 ends end VERB bjmsr-311 301 4 when when SCONJ bjmsr-311 301 5 we we PRON bjmsr-311 301 6 can can AUX bjmsr-311 301 7 not not PART bjmsr-311 301 8 enter enter VERB bjmsr-311 301 9 any any DET bjmsr-311 301 10 new new ADJ bjmsr-311 301 11 point point NOUN bjmsr-311 301 12 to to PART bjmsr-311 301 13 reduce reduce VERB bjmsr-311 301 14 the the DET bjmsr-311 301 15 objective objective ADJ bjmsr-311 301 16 function function NOUN bjmsr-311 301 17 value value NOUN bjmsr-311 301 18 . . PUNCT bjmsr-311 302 1 in in ADP bjmsr-311 302 2 this this DET bjmsr-311 302 3 context context NOUN bjmsr-311 302 4 , , PUNCT bjmsr-311 302 5 it it PRON bjmsr-311 302 6 is be AUX bjmsr-311 302 7 similar similar ADJ bjmsr-311 302 8 to to ADP bjmsr-311 302 9 the the DET bjmsr-311 302 10 simplex simplex NOUN bjmsr-311 302 11 procedure procedure NOUN bjmsr-311 302 12 of of ADP bjmsr-311 302 13 linear linear ADJ bjmsr-311 302 14 programming programming NOUN bjmsr-311 302 15 technique technique NOUN bjmsr-311 302 16 . . PUNCT bjmsr-311 303 1 algorithm algorithm NOUN bjmsr-311 303 2 4 4 NUM bjmsr-311 303 3 is be AUX bjmsr-311 303 4 also also ADV bjmsr-311 303 5 a a DET bjmsr-311 303 6 descent descent NOUN bjmsr-311 303 7 method method NOUN bjmsr-311 303 8 . . PUNCT bjmsr-311 304 1 because because SCONJ bjmsr-311 304 2 in in ADP bjmsr-311 304 3 each each DET bjmsr-311 304 4 iteration iteration NOUN bjmsr-311 304 5 the the DET bjmsr-311 304 6 value value NOUN bjmsr-311 304 7 of of ADP bjmsr-311 304 8 s s NOUN bjmsr-311 304 9 is be AUX bjmsr-311 304 10 decreased decrease VERB bjmsr-311 304 11 . . PUNCT bjmsr-311 305 1 the the DET bjmsr-311 305 2 proof proof NOUN bjmsr-311 305 3 is be AUX bjmsr-311 305 4 completely completely ADV bjmsr-311 305 5 similar similar ADJ bjmsr-311 305 6 to to ADP bjmsr-311 305 7 that that PRON bjmsr-311 305 8 of of ADP bjmsr-311 305 9 algorithm algorithm NOUN bjmsr-311 305 10 3 3 NUM bjmsr-311 305 11 stated state VERB bjmsr-311 305 12 before before ADV bjmsr-311 305 13 . . PUNCT bjmsr-311 306 1 the the DET bjmsr-311 306 2 main main ADJ bjmsr-311 306 3 difference difference NOUN bjmsr-311 306 4 of of ADP bjmsr-311 306 5 this this DET bjmsr-311 306 6 algorithm algorithm NOUN bjmsr-311 306 7 with with ADP bjmsr-311 306 8 algorithm algorithm NOUN bjmsr-311 306 9 3 3 NUM bjmsr-311 306 10 is be AUX bjmsr-311 306 11 in in ADP bjmsr-311 306 12 choosing choose VERB bjmsr-311 306 13 the the DET bjmsr-311 306 14 point point NOUN bjmsr-311 306 15 which which PRON bjmsr-311 306 16 should should AUX bjmsr-311 306 17 be be AUX bjmsr-311 306 18 deleted delete VERB bjmsr-311 306 19 from from ADP bjmsr-311 306 20 the the DET bjmsr-311 306 21 basis basis NOUN bjmsr-311 306 22 . . PUNCT bjmsr-311 307 1 therefore therefore ADV bjmsr-311 307 2 , , PUNCT bjmsr-311 307 3 in in ADP bjmsr-311 307 4 each each DET bjmsr-311 307 5 step step NOUN bjmsr-311 307 6 , , PUNCT bjmsr-311 307 7 we we PRON bjmsr-311 307 8 need need AUX bjmsr-311 307 9 not not PART bjmsr-311 307 10 keep keep VERB bjmsr-311 307 11 some some DET bjmsr-311 307 12 points point NOUN bjmsr-311 307 13 in in ADP bjmsr-311 307 14 the the DET bjmsr-311 307 15 basis basis NOUN bjmsr-311 307 16 to to PART bjmsr-311 307 17 solve solve VERB bjmsr-311 307 18 smaller small ADJ bjmsr-311 307 19 size size NOUN bjmsr-311 307 20 models model NOUN bjmsr-311 307 21 . . PUNCT bjmsr-311 308 1 on on ADP bjmsr-311 308 2 the the DET bjmsr-311 308 3 other other ADJ bjmsr-311 308 4 hand hand NOUN bjmsr-311 308 5 , , PUNCT bjmsr-311 308 6 in in ADP bjmsr-311 308 7 each each DET bjmsr-311 308 8 m m NOUN bjmsr-311 308 9 iterations iteration NOUN bjmsr-311 308 10 , , PUNCT bjmsr-311 308 11 all all PRON bjmsr-311 308 12 m m VERB bjmsr-311 308 13 points point NOUN bjmsr-311 308 14 in in ADP bjmsr-311 308 15 the the DET bjmsr-311 308 16 basis basis NOUN bjmsr-311 308 17 are be AUX bjmsr-311 308 18 discarded discard VERB bjmsr-311 308 19 , , PUNCT bjmsr-311 308 20 and and CCONJ bjmsr-311 308 21 new new ADJ bjmsr-311 308 22 points point NOUN bjmsr-311 308 23 enter enter VERB bjmsr-311 308 24 . . PUNCT bjmsr-311 309 1 in in ADP bjmsr-311 309 2 algorithm algorithm NOUN bjmsr-311 309 3 3 3 NUM bjmsr-311 309 4 , , PUNCT bjmsr-311 309 5 we we PRON bjmsr-311 309 6 kept keep VERB bjmsr-311 309 7 some some DET bjmsr-311 309 8 points point NOUN bjmsr-311 309 9 in in ADP bjmsr-311 309 10 the the DET bjmsr-311 309 11 basis basis NOUN bjmsr-311 309 12 until until SCONJ bjmsr-311 309 13 we we PRON bjmsr-311 309 14 reach reach VERB bjmsr-311 309 15 an an DET bjmsr-311 309 16 optimal optimal ADJ bjmsr-311 309 17 point point NOUN bjmsr-311 309 18 for for ADP bjmsr-311 309 19 smaller small ADJ bjmsr-311 309 20 size size NOUN bjmsr-311 309 21 reduced reduce VERB bjmsr-311 309 22 model model NOUN bjmsr-311 309 23 . . PUNCT bjmsr-311 310 1 it it PRON bjmsr-311 310 2 should should AUX bjmsr-311 310 3 be be AUX bjmsr-311 310 4 noted note VERB bjmsr-311 310 5 that that SCONJ bjmsr-311 310 6 one one NUM bjmsr-311 310 7 point point NOUN bjmsr-311 310 8 may may AUX bjmsr-311 310 9 be be AUX bjmsr-311 310 10 discarded discard VERB bjmsr-311 310 11 and and CCONJ bjmsr-311 310 12 reenter reenter VERB bjmsr-311 310 13 the the DET bjmsr-311 310 14 basis basis NOUN bjmsr-311 310 15 through through ADP bjmsr-311 310 16 m m NOUN bjmsr-311 310 17 iterations iteration NOUN bjmsr-311 310 18 . . PUNCT bjmsr-311 311 1 this this PRON bjmsr-311 311 2 is be AUX bjmsr-311 311 3 not not PART bjmsr-311 311 4 contradictory contradictory ADJ bjmsr-311 311 5 and and CCONJ bjmsr-311 311 6 actually actually ADV bjmsr-311 311 7 occurs occur VERB bjmsr-311 311 8 , , PUNCT bjmsr-311 311 9 especially especially ADV bjmsr-311 311 10 when when SCONJ bjmsr-311 311 11 we we PRON bjmsr-311 311 12 are be AUX bjmsr-311 311 13 near near ADP bjmsr-311 311 14 the the DET bjmsr-311 311 15 optimal optimal ADJ bjmsr-311 311 16 solution solution NOUN bjmsr-311 311 17 . . PUNCT bjmsr-311 312 1 as as SCONJ bjmsr-311 312 2 we we PRON bjmsr-311 312 3 will will AUX bjmsr-311 312 4 see see VERB bjmsr-311 312 5 in in ADP bjmsr-311 312 6 the the DET bjmsr-311 312 7 forthcoming forthcoming ADJ bjmsr-311 312 8 section section NOUN bjmsr-311 312 9 , , PUNCT bjmsr-311 312 10 due due ADP bjmsr-311 312 11 to to ADP bjmsr-311 312 12 different different ADJ bjmsr-311 312 13 properties property NOUN bjmsr-311 312 14 of of ADP bjmsr-311 312 15 this this DET bjmsr-311 312 16 algorithm algorithm NOUN bjmsr-311 312 17 , , PUNCT bjmsr-311 312 18 many many ADJ bjmsr-311 312 19 manipulations manipulation NOUN bjmsr-311 312 20 in in ADP bjmsr-311 312 21 computational computational ADJ bjmsr-311 312 22 steps step NOUN bjmsr-311 312 23 may may AUX bjmsr-311 312 24 be be AUX bjmsr-311 312 25 adopted adopt VERB bjmsr-311 312 26 to to PART bjmsr-311 312 27 start start VERB bjmsr-311 312 28 calculations calculation NOUN bjmsr-311 312 29 . . PUNCT bjmsr-311 313 1 before before ADP bjmsr-311 313 2 making make VERB bjmsr-311 313 3 this this DET bjmsr-311 313 4 algorithm algorithm NOUN bjmsr-311 313 5 more more ADV bjmsr-311 313 6 sophisticated sophisticated ADJ bjmsr-311 313 7 , , PUNCT bjmsr-311 313 8 it it PRON bjmsr-311 313 9 is be AUX bjmsr-311 313 10 suitable suitable ADJ bjmsr-311 313 11 to to PART bjmsr-311 313 12 summarize summarize VERB bjmsr-311 313 13 its its PRON bjmsr-311 313 14 general general ADJ bjmsr-311 313 15 steps step NOUN bjmsr-311 313 16 as as SCONJ bjmsr-311 313 17 follows follow VERB bjmsr-311 313 18 . . PUNCT bjmsr-311 314 1 algorithm algorithm NOUN bjmsr-311 314 2 4 4 NUM bjmsr-311 314 3 step step NOUN bjmsr-311 314 4 0 0 NUM bjmsr-311 314 5 ) ) PUNCT bjmsr-311 314 6 select select ADJ bjmsr-311 314 7 arbitrary arbitrary ADJ bjmsr-311 314 8 points point NOUN bjmsr-311 314 9 k1, k1, NOUN bjmsr-311 314 10 ... ... PUNCT bjmsr-311 314 11 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 314 12 ) ) PUNCT bjmsr-311 314 13 . . PUNCT bjmsr-311 315 1 step step NOUN bjmsr-311 315 2 1 1 NUM bjmsr-311 315 3 ) ) PUNCT bjmsr-311 315 4 proceed proceed VERB bjmsr-311 315 5 the the DET bjmsr-311 315 6 transformations transformation NOUN bjmsr-311 315 7 ( ( PUNCT bjmsr-311 315 8 63 63 NUM bjmsr-311 315 9 ) ) PUNCT bjmsr-311 315 10 through through ADP bjmsr-311 315 11 ( ( PUNCT bjmsr-311 315 12 65 65 NUM bjmsr-311 315 13 ) ) PUNCT bjmsr-311 315 14 to to PART bjmsr-311 315 15 reduce reduce VERB bjmsr-311 315 16 the the DET bjmsr-311 315 17 model model NOUN bjmsr-311 315 18 to to ADP bjmsr-311 315 19 one one NUM bjmsr-311 315 20 - - PUNCT bjmsr-311 315 21 parameter parameter NOUN bjmsr-311 315 22 transformed transform VERB bjmsr-311 315 23 restricted restrict VERB bjmsr-311 315 24 linear linear NOUN bjmsr-311 315 25 model model NOUN bjmsr-311 315 26 . . PUNCT bjmsr-311 316 1 step step NOUN bjmsr-311 316 2 2 2 NUM bjmsr-311 316 3 ) ) PUNCT bjmsr-311 316 4 apply apply VERB bjmsr-311 316 5 weighted weight VERB bjmsr-311 316 6 median median ADJ bjmsr-311 316 7 procedure procedure NOUN bjmsr-311 316 8 to to PART bjmsr-311 316 9 find find VERB bjmsr-311 316 10 the the DET bjmsr-311 316 11 point point NOUN bjmsr-311 316 12 m. m. NOUN bjmsr-311 316 13 step step NOUN bjmsr-311 316 14 3 3 NUM bjmsr-311 316 15 ) ) PUNCT bjmsr-311 316 16 assign assign NOUN bjmsr-311 316 17 m m PROPN bjmsr-311 316 18 to to ADP bjmsr-311 316 19 one one NUM bjmsr-311 316 20 of of ADP bjmsr-311 316 21 the the DET bjmsr-311 316 22 k1, k1, NOUN bjmsr-311 316 23 ... ... PUNCT bjmsr-311 316 24 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 316 25 ) ) PUNCT bjmsr-311 316 26 which which PRON bjmsr-311 316 27 is be AUX bjmsr-311 316 28 oldest old ADJ bjmsr-311 316 29 in in ADP bjmsr-311 316 30 the the DET bjmsr-311 316 31 basis basis NOUN bjmsr-311 316 32 . . PUNCT bjmsr-311 317 1 step step NOUN bjmsr-311 317 2 4 4 NUM bjmsr-311 317 3 ) ) PUNCT bjmsr-311 317 4 check check NOUN bjmsr-311 317 5 if if SCONJ bjmsr-311 317 6 the the DET bjmsr-311 317 7 newly newly ADV bjmsr-311 317 8 found find VERB bjmsr-311 317 9 point point NOUN bjmsr-311 317 10 m m VERB bjmsr-311 317 11 which which PRON bjmsr-311 317 12 enters enter VERB bjmsr-311 317 13 the the DET bjmsr-311 317 14 basis basis NOUN bjmsr-311 317 15 , , PUNCT bjmsr-311 317 16 discard discard VERB bjmsr-311 317 17 the the DET bjmsr-311 317 18 point point NOUN bjmsr-311 317 19 which which PRON bjmsr-311 317 20 entered enter VERB bjmsr-311 317 21 in in ADP bjmsr-311 317 22 the the DET bjmsr-311 317 23 previous previous ADJ bjmsr-311 317 24 iteration iteration NOUN bjmsr-311 317 25 repeats repeat NOUN bjmsr-311 317 26 m-1 m-1 PROPN bjmsr-311 317 27 times time NOUN bjmsr-311 317 28 then then ADV bjmsr-311 317 29 go go VERB bjmsr-311 317 30 to to PART bjmsr-311 317 31 step step VERB bjmsr-311 317 32 5 5 NUM bjmsr-311 317 33 ; ; PUNCT bjmsr-311 317 34 otherwise otherwise ADV bjmsr-311 317 35 go go VERB bjmsr-311 317 36 to to ADP bjmsr-311 317 37 step1 step1 PROPN bjmsr-311 317 38 . . PUNCT bjmsr-311 318 1 step step NOUN bjmsr-311 318 2 5 5 NUM bjmsr-311 318 3 ) ) PUNCT bjmsr-311 318 4 set set VERB bjmsr-311 318 5 k(m)=m k(m)=m NOUN bjmsr-311 318 6 . . PUNCT bjmsr-311 318 7 by by ADP bjmsr-311 318 8 using use VERB bjmsr-311 318 9 the the DET bjmsr-311 318 10 final final ADJ bjmsr-311 318 11 values value NOUN bjmsr-311 318 12 of of ADP bjmsr-311 318 13 k1, k1, NOUN bjmsr-311 318 14 ... ... PUNCT bjmsr-311 318 15 ,k(m ,k(m PUNCT bjmsr-311 318 16 ) ) PUNCT bjmsr-311 318 17 , , PUNCT bjmsr-311 318 18 solve solve VERB bjmsr-311 318 19 the the DET bjmsr-311 318 20 following follow VERB bjmsr-311 318 21 system system NOUN bjmsr-311 318 22 of of ADP bjmsr-311 318 23 equations equation NOUN bjmsr-311 318 24 for for ADP bjmsr-311 318 25 ß ß DET bjmsr-311 318 26 j^ j^ NOUN bjmsr-311 318 27 , , PUNCT bjmsr-311 318 28 for for ADP bjmsr-311 318 29 j=1, j=1, NOUN bjmsr-311 318 30 ... ... PUNCT bjmsr-311 318 31 ,m ,m PUNCT bjmsr-311 318 32 ; ; PUNCT bjmsr-311 318 33 m m PROPN bjmsr-311 318 34 σ σ NUM bjmsr-311 318 35 ßj^xjki ßj^xjki PROPN bjmsr-311 318 36 = = SYM bjmsr-311 318 37 yki yki NOUN bjmsr-311 318 38 i=1, i=1, NOUN bjmsr-311 318 39 ... ... PUNCT bjmsr-311 318 40 ,m ,m PUNCT bjmsr-311 318 41 j=1 j=1 PROPN bjmsr-311 318 42 stop stop VERB bjmsr-311 318 43 . . PUNCT bjmsr-311 319 1 after after ADP bjmsr-311 319 2 discussing discuss VERB bjmsr-311 319 3 the the DET bjmsr-311 319 4 properties property NOUN bjmsr-311 319 5 of of ADP bjmsr-311 319 6 algorithm algorithm NOUN bjmsr-311 319 7 4 4 NUM bjmsr-311 319 8 , , PUNCT bjmsr-311 319 9 we we PRON bjmsr-311 319 10 will will AUX bjmsr-311 319 11 give give VERB bjmsr-311 319 12 more more ADJ bjmsr-311 319 13 expository expository ADJ bjmsr-311 319 14 steps step NOUN bjmsr-311 319 15 of of ADP bjmsr-311 319 16 computation computation NOUN bjmsr-311 319 17 for for ADP bjmsr-311 319 18 this this DET bjmsr-311 319 19 algorithm algorithm NOUN bjmsr-311 319 20 . . PUNCT bjmsr-311 320 1 by by ADP bjmsr-311 320 2 using use VERB bjmsr-311 320 3 these these DET bjmsr-311 320 4 properties property NOUN bjmsr-311 320 5 , , PUNCT bjmsr-311 320 6 we we PRON bjmsr-311 320 7 can can AUX bjmsr-311 320 8 make make VERB bjmsr-311 320 9 this this DET bjmsr-311 320 10 algorithm algorithm NOUN bjmsr-311 320 11 more more ADV bjmsr-311 320 12 efficient efficient ADJ bjmsr-311 320 13 . . PUNCT bjmsr-311 321 1 4.3 4.3 NUM bjmsr-311 321 2 properties property NOUN bjmsr-311 321 3 before before ADP bjmsr-311 321 4 discussing discuss VERB bjmsr-311 321 5 the the DET bjmsr-311 321 6 properties property NOUN bjmsr-311 321 7 of of ADP bjmsr-311 321 8 the the DET bjmsr-311 321 9 proposed propose VERB bjmsr-311 321 10 algorithms algorithms NOUN bjmsr-311 321 11 specifically specifically ADV bjmsr-311 321 12 algorithm algorithm VERB bjmsr-311 321 13 4 4 NUM bjmsr-311 321 14 , , PUNCT bjmsr-311 321 15 let let VERB bjmsr-311 321 16 us we PRON bjmsr-311 321 17 consider consider VERB bjmsr-311 321 18 the the PRON bjmsr-311 321 19 following follow VERB bjmsr-311 321 20 four four NUM bjmsr-311 321 21 parameters parameter NOUN bjmsr-311 321 22 model model NOUN bjmsr-311 321 23 l1 l1 PROPN bjmsr-311 321 24 norm norm PROPN bjmsr-311 321 25 objective objective ADJ bjmsr-311 321 26 function function NOUN bjmsr-311 321 27 , , PUNCT bjmsr-311 321 28 n n PROPN bjmsr-311 321 29 s s NOUN bjmsr-311 321 30 = = SYM bjmsr-311 321 31 σ σ PROPN bjmsr-311 321 32 │ │ NOUN bjmsr-311 321 33 yi yi PROPN bjmsr-311 321 34 - - PUNCT bjmsr-311 321 35 ß0 ß0 NOUN bjmsr-311 321 36 - - PUNCT bjmsr-311 321 37 ß1x1i ß1x1i NUM bjmsr-311 321 38 - - PUNCT bjmsr-311 321 39 ß2x2i ß2x2i NUM bjmsr-311 321 40 - - PUNCT bjmsr-311 321 41 ß3x3i ß3x3i VERB bjmsr-311 321 42 │ │ X bjmsr-311 321 43 ( ( PUNCT bjmsr-311 321 44 66 66 NUM bjmsr-311 321 45 ) ) PUNCT bjmsr-311 321 46 i=1 i=1 ADP bjmsr-311 321 47 some some DET bjmsr-311 321 48 steps step NOUN bjmsr-311 321 49 should should AUX bjmsr-311 321 50 be be AUX bjmsr-311 321 51 taken take VERB bjmsr-311 321 52 to to PART bjmsr-311 321 53 reduce reduce VERB bjmsr-311 321 54 ( ( PUNCT bjmsr-311 321 55 66 66 NUM bjmsr-311 321 56 ) ) PUNCT bjmsr-311 321 57 to to ADP bjmsr-311 321 58 a a DET bjmsr-311 321 59 weighted weight VERB bjmsr-311 321 60 median median ADJ bjmsr-311 321 61 problem problem NOUN bjmsr-311 321 62 by by ADP bjmsr-311 321 63 entering enter VERB bjmsr-311 321 64 three three NUM bjmsr-311 321 65 arbitrary arbitrary ADJ bjmsr-311 321 66 integers integer NOUN bjmsr-311 321 67 k1 k1 NOUN bjmsr-311 321 68 , , PUNCT bjmsr-311 321 69 k2 k2 NOUN bjmsr-311 321 70 , , PUNCT bjmsr-311 321 71 k3 k3 VERB bjmsr-311 321 72 between between ADP bjmsr-311 321 73 one one NUM bjmsr-311 321 74 and and CCONJ bjmsr-311 321 75 n n NOUN bjmsr-311 321 76 as as SCONJ bjmsr-311 321 77 follows follow VERB bjmsr-311 321 78 . . PUNCT bjmsr-311 322 1 note note VERB bjmsr-311 322 2 that that DET bjmsr-311 322 3 function function NOUN bjmsr-311 322 4 ( ( PUNCT bjmsr-311 322 5 1 1 X bjmsr-311 322 6 ) ) PUNCT bjmsr-311 322 7 has have AUX bjmsr-311 322 8 been be AUX bjmsr-311 322 9 slightly slightly ADV bjmsr-311 322 10 redefined redefine VERB bjmsr-311 322 11 to to PART bjmsr-311 322 12 include include VERB bjmsr-311 322 13 intercept intercept NOUN bjmsr-311 322 14 as as ADP bjmsr-311 322 15 a a DET bjmsr-311 322 16 simple simple ADJ bjmsr-311 322 17 term term NOUN bjmsr-311 322 18 , , PUNCT bjmsr-311 322 19 in in ADP bjmsr-311 322 20 equation equation NOUN bjmsr-311 322 21 ( ( PUNCT bjmsr-311 322 22 66 66 NUM bjmsr-311 322 23 ) ) PUNCT bjmsr-311 322 24 . . PUNCT bjmsr-311 323 1 similar similar ADJ bjmsr-311 323 2 to to ADP bjmsr-311 323 3 the the DET bjmsr-311 323 4 transformations transformation NOUN bjmsr-311 323 5 ( ( PUNCT bjmsr-311 323 6 63 63 NUM bjmsr-311 323 7 ) ) PUNCT bjmsr-311 323 8 through through ADP bjmsr-311 323 9 ( ( PUNCT bjmsr-311 323 10 65 65 NUM bjmsr-311 323 11 ) ) PUNCT bjmsr-311 323 12 , , PUNCT bjmsr-311 323 13 the the DET bjmsr-311 323 14 following follow VERB bjmsr-311 323 15 steps step NOUN bjmsr-311 323 16 are be AUX bjmsr-311 323 17 taken take VERB bjmsr-311 323 18 sequentially sequentially ADV bjmsr-311 323 19 . . PUNCT bjmsr-311 324 1 deviate deviate VERB bjmsr-311 324 2 all all DET bjmsr-311 324 3 observations observation NOUN bjmsr-311 324 4 from from ADP bjmsr-311 324 5 k1th k1th PROPN bjmsr-311 324 6 observation observation NOUN bjmsr-311 324 7 , , PUNCT bjmsr-311 324 8 yi yi PROPN bjmsr-311 324 9 k1 k1 PROPN bjmsr-311 324 10 = = SYM bjmsr-311 324 11 yi yi PROPN bjmsr-311 324 12 yk1 yk1 PROPN bjmsr-311 324 13 i=1, i=1, PROPN bjmsr-311 324 14 ... ... PUNCT bjmsr-311 324 15 ,n ,n PUNCT bjmsr-311 324 16 ( ( PUNCT bjmsr-311 324 17 67 67 NUM bjmsr-311 325 1 ) ) PUNCT bjmsr-311 325 2 xji xji PROPN bjmsr-311 325 3 k1 k1 NOUN bjmsr-311 325 4 = = PUNCT bjmsr-311 325 5 xji xji PROPN bjmsr-311 325 6 xjk1 xjk1 PROPN bjmsr-311 325 7 i=1, i=1, PROPN bjmsr-311 325 8 ... ... PUNCT bjmsr-311 325 9 ,n ,n PROPN bjmsr-311 325 10 ; ; PUNCT bjmsr-311 325 11 j=1,2,3 j=1,2,3 NUM bjmsr-311 325 12 ( ( PUNCT bjmsr-311 325 13 68 68 NUM bjmsr-311 325 14 ) ) PUNCT bjmsr-311 325 15 the the DET bjmsr-311 325 16 objective objective ADJ bjmsr-311 325 17 function function NOUN bjmsr-311 325 18 becomes become VERB bjmsr-311 325 19 , , PUNCT bjmsr-311 325 20 n n PRON bjmsr-311 325 21 copyright copyright NOUN bjmsr-311 325 22 © © PROPN bjmsr-311 325 23 cc cc NOUN bjmsr-311 325 24 - - PUNCT bjmsr-311 325 25 by by ADP bjmsr-311 325 26 - - PUNCT bjmsr-311 325 27 nc nc PROPN bjmsr-311 325 28 2019 2019 NUM bjmsr-311 325 29 , , PUNCT bjmsr-311 325 30 bjmsr bjmsr PROPN bjmsr-311 325 31 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 325 32 bangladesh bangladesh PROPN bjmsr-311 325 33 journal journal PROPN bjmsr-311 325 34 of of ADP bjmsr-311 325 35 multidisciplinary multidisciplinary ADJ bjmsr-311 325 36 scientific scientific ADJ bjmsr-311 325 37 research research NOUN bjmsr-311 325 38 vol vol NOUN bjmsr-311 325 39 . . PROPN bjmsr-311 326 1 1 1 NUM bjmsr-311 326 2 , , PUNCT bjmsr-311 326 3 no no INTJ bjmsr-311 326 4 . . NOUN bjmsr-311 326 5 1 1 NUM bjmsr-311 326 6 ; ; PUNCT bjmsr-311 326 7 2019 2019 NUM bjmsr-311 326 8 12 12 NUM bjmsr-311 326 9 sk1 sk1 PROPN bjmsr-311 326 10 = = PROPN bjmsr-311 326 11 σ σ PROPN bjmsr-311 326 12 │ │ NOUN bjmsr-311 326 13 yi yi PROPN bjmsr-311 326 14 k1 k1 PROPN bjmsr-311 326 15 - - PUNCT bjmsr-311 326 16 ß1 ß1 NOUN bjmsr-311 326 17 - - PUNCT bjmsr-311 326 18 ß2x2i ß2x2i NUM bjmsr-311 326 19 k1 k1 NOUN bjmsr-311 326 20 - - PUNCT bjmsr-311 326 21 ß3x3i ß3x3i NOUN bjmsr-311 326 22 k1 k1 NOUN bjmsr-311 326 23 │ │ X bjmsr-311 326 24 ( ( PUNCT bjmsr-311 326 25 69 69 NUM bjmsr-311 326 26 ) ) PUNCT bjmsr-311 327 1 i=1 i=1 PROPN bjmsr-311 327 2 divide divide PROPN bjmsr-311 327 3 yik1 yik1 PROPN bjmsr-311 328 1 and and CCONJ bjmsr-311 328 2 xji xji PROPN bjmsr-311 328 3 k1 k1 PROPN bjmsr-311 328 4 for for ADP bjmsr-311 328 5 j=2,3 j=2,3 NOUN bjmsr-311 328 6 by by ADP bjmsr-311 328 7 x1i x1i PROPN bjmsr-311 328 8 k1 k1 PROPN bjmsr-311 328 9 for for ADP bjmsr-311 328 10 all all DET bjmsr-311 328 11 i=1, i=1, NOUN bjmsr-311 328 12 ... ... PUNCT bjmsr-311 328 13 ,n ,n NOUN bjmsr-311 328 14 ; ; PUNCT bjmsr-311 328 15 yi yi PROPN bjmsr-311 328 16 s1 s1 NOUN bjmsr-311 328 17 = = PROPN bjmsr-311 328 18 yi yi PROPN bjmsr-311 328 19 k1 k1 PROPN bjmsr-311 328 20 / / SYM bjmsr-311 328 21 x1i x1i PROPN bjmsr-311 328 22 k1 k1 PROPN bjmsr-311 328 23 i=1, i=1, PROPN bjmsr-311 328 24 ... ... PUNCT bjmsr-311 328 25 ,n ,n PUNCT bjmsr-311 328 26 ( ( PUNCT bjmsr-311 328 27 70 70 NUM bjmsr-311 328 28 ) ) PUNCT bjmsr-311 328 29 xji xji PROPN bjmsr-311 329 1 s1 s1 NOUN bjmsr-311 329 2 = = PUNCT bjmsr-311 329 3 xji xji PROPN bjmsr-311 329 4 k1 k1 PROPN bjmsr-311 329 5 / / SYM bjmsr-311 329 6 x1i x1i PROPN bjmsr-311 329 7 k1 k1 PROPN bjmsr-311 329 8 i=1, i=1, PROPN bjmsr-311 329 9 ... ... PUNCT bjmsr-311 329 10 ,n ,n PUNCT bjmsr-311 329 11 ; ; PUNCT bjmsr-311 329 12 j=2,3 j=2,3 NOUN bjmsr-311 329 13 ( ( PUNCT bjmsr-311 329 14 71 71 NUM bjmsr-311 329 15 ) ) PUNCT bjmsr-311 329 16 the the DET bjmsr-311 329 17 objective objective ADJ bjmsr-311 329 18 function function NOUN bjmsr-311 329 19 becomes become VERB bjmsr-311 329 20 , , PUNCT bjmsr-311 329 21 n n PROPN bjmsr-311 329 22 sk1 sk1 NOUN bjmsr-311 329 23 = = PROPN bjmsr-311 329 24 σ σ PROPN bjmsr-311 329 25 │ │ PROPN bjmsr-311 329 26 x1i x1i PROPN bjmsr-311 329 27 k1 k1 NOUN bjmsr-311 329 28 │ │ VERB bjmsr-311 329 29 │ │ NOUN bjmsr-311 329 30 yi yi NOUN bjmsr-311 329 31 s1 s1 NOUN bjmsr-311 329 32 - - PUNCT bjmsr-311 329 33 ß1 ß1 NOUN bjmsr-311 329 34 - - PUNCT bjmsr-311 329 35 ß2x2i ß2x2i NUM bjmsr-311 329 36 s1 s1 NOUN bjmsr-311 329 37 - - PUNCT bjmsr-311 329 38 ß3x3i ß3x3i NOUN bjmsr-311 329 39 s1 s1 NOUN bjmsr-311 329 40 │ │ X bjmsr-311 329 41 ( ( PUNCT bjmsr-311 329 42 72 72 NUM bjmsr-311 329 43 ) ) PUNCT bjmsr-311 329 44 i=1 i=1 VERB bjmsr-311 329 45 deviate deviate VERB bjmsr-311 329 46 yi yi PROPN bjmsr-311 329 47 and and CCONJ bjmsr-311 329 48 xji xji PROPN bjmsr-311 329 49 s1 s1 PROPN bjmsr-311 329 50 for for ADP bjmsr-311 329 51 j=2,3 j=2,3 NOUN bjmsr-311 329 52 from from ADP bjmsr-311 329 53 k2th k2th NOUN bjmsr-311 329 54 observation observation NOUN bjmsr-311 329 55 , , PUNCT bjmsr-311 329 56 yi yi PROPN bjmsr-311 329 57 k2 k2 PROPN bjmsr-311 329 58 = = PROPN bjmsr-311 329 59 yi yi PROPN bjmsr-311 329 60 s1 s1 PROPN bjmsr-311 329 61 -yk2 -yk2 PUNCT bjmsr-311 329 62 s1 s1 PROPN bjmsr-311 329 63 i=1, i=1, PROPN bjmsr-311 329 64 ... ... PUNCT bjmsr-311 329 65 ,n ,n PUNCT bjmsr-311 329 66 ( ( PUNCT bjmsr-311 329 67 73 73 NUM bjmsr-311 329 68 ) ) PUNCT bjmsr-311 330 1 xji xji PROPN bjmsr-311 330 2 k2 k2 PROPN bjmsr-311 330 3 = = PUNCT bjmsr-311 331 1 xji xji PROPN bjmsr-311 331 2 s1 s1 PROPN bjmsr-311 331 3 xjk2 xjk2 PROPN bjmsr-311 331 4 s1 s1 PROPN bjmsr-311 331 5 i=1, i=1, PROPN bjmsr-311 331 6 ... ... PUNCT bjmsr-311 331 7 ,n ,n NOUN bjmsr-311 331 8 , , PUNCT bjmsr-311 331 9 j=2,3 j=2,3 NOUN bjmsr-311 331 10 ( ( PUNCT bjmsr-311 331 11 74 74 NUM bjmsr-311 331 12 ) ) PUNCT bjmsr-311 331 13 the the DET bjmsr-311 331 14 objective objective ADJ bjmsr-311 331 15 function function NOUN bjmsr-311 331 16 reduces reduce VERB bjmsr-311 331 17 to to ADP bjmsr-311 331 18 , , PUNCT bjmsr-311 331 19 n n PRON bjmsr-311 331 20 sk1k2 sk1k2 PROPN bjmsr-311 331 21 = = PROPN bjmsr-311 331 22 σ σ PROPN bjmsr-311 331 23 │ │ PROPN bjmsr-311 331 24 x1i x1i PROPN bjmsr-311 331 25 k1 k1 NOUN bjmsr-311 331 26 │ │ VERB bjmsr-311 331 27 │ │ NOUN bjmsr-311 331 28 yi yi NOUN bjmsr-311 331 29 k2 k2 PROPN bjmsr-311 331 30 - - PUNCT bjmsr-311 331 31 ß2x2i ß2x2i NOUN bjmsr-311 331 32 k2 k2 PROPN bjmsr-311 331 33 - - PUNCT bjmsr-311 331 34 ß3x3i ß3x3i X bjmsr-311 331 35 k2 k2 ADJ bjmsr-311 331 36 │ │ X bjmsr-311 331 37 ( ( PUNCT bjmsr-311 331 38 75 75 NUM bjmsr-311 331 39 ) ) PUNCT bjmsr-311 331 40 i=1 i=1 PROPN bjmsr-311 331 41 divide divide VERB bjmsr-311 331 42 yi yi PROPN bjmsr-311 331 43 k2 k2 PROPN bjmsr-311 331 44 and and CCONJ bjmsr-311 331 45 xji xji PROPN bjmsr-311 331 46 k2 k2 PROPN bjmsr-311 331 47 for for ADP bjmsr-311 331 48 j=3 j=3 PROPN bjmsr-311 331 49 by by ADP bjmsr-311 331 50 x2i x2i PROPN bjmsr-311 331 51 k2 k2 PROPN bjmsr-311 331 52 for for ADP bjmsr-311 331 53 all all DET bjmsr-311 331 54 i=1, i=1, NOUN bjmsr-311 331 55 .. .. PUNCT bjmsr-311 331 56 ,n ,n NOUN bjmsr-311 331 57 ; ; PUNCT bjmsr-311 331 58 yi yi PROPN bjmsr-311 331 59 s2 s2 PROPN bjmsr-311 331 60 = = PUNCT bjmsr-311 331 61 yi yi PROPN bjmsr-311 331 62 k2 k2 PROPN bjmsr-311 331 63 / / SYM bjmsr-311 331 64 x2i x2i PROPN bjmsr-311 331 65 k2 k2 PROPN bjmsr-311 331 66 i=1, i=1, PROPN bjmsr-311 331 67 ... ... PUNCT bjmsr-311 331 68 ,n ,n PUNCT bjmsr-311 331 69 ( ( PUNCT bjmsr-311 331 70 76 76 NUM bjmsr-311 331 71 ) ) PUNCT bjmsr-311 332 1 xji xji PROPN bjmsr-311 332 2 s2 s2 NOUN bjmsr-311 332 3 = = PUNCT bjmsr-311 332 4 xji xji PROPN bjmsr-311 332 5 k2 k2 PROPN bjmsr-311 332 6 / / SYM bjmsr-311 332 7 x2i x2i PROPN bjmsr-311 332 8 k2 k2 PROPN bjmsr-311 332 9 i=1, i=1, PROPN bjmsr-311 332 10 ... ... PUNCT bjmsr-311 332 11 ,n ,n PROPN bjmsr-311 332 12 ; ; PUNCT bjmsr-311 332 13 j=3 j=3 PROPN bjmsr-311 332 14 ( ( PUNCT bjmsr-311 332 15 77 77 NUM bjmsr-311 332 16 ) ) PUNCT bjmsr-311 332 17 the the DET bjmsr-311 332 18 objective objective ADJ bjmsr-311 332 19 function function NOUN bjmsr-311 332 20 forms form NOUN bjmsr-311 332 21 as as ADP bjmsr-311 332 22 , , PUNCT bjmsr-311 332 23 n n PRON bjmsr-311 332 24 sk1k2 sk1k2 PROPN bjmsr-311 332 25 = = PROPN bjmsr-311 332 26 σ σ PROPN bjmsr-311 332 27 │ │ PROPN bjmsr-311 332 28 x1i x1i PROPN bjmsr-311 332 29 k1x2i k1x2i PUNCT bjmsr-311 332 30 k2 k2 X bjmsr-311 332 31 │ │ VERB bjmsr-311 332 32 │ │ ADJ bjmsr-311 332 33 yi yi NOUN bjmsr-311 332 34 s2 s2 PROPN bjmsr-311 332 35 - - PUNCT bjmsr-311 332 36 ß2 ß2 VERB bjmsr-311 332 37 - - PUNCT bjmsr-311 332 38 ß3x3i ß3x3i NOUN bjmsr-311 332 39 s2 s2 PROPN bjmsr-311 332 40 │ │ X bjmsr-311 332 41 ( ( PUNCT bjmsr-311 332 42 78 78 NUM bjmsr-311 332 43 ) ) PUNCT bjmsr-311 332 44 i=1 i=1 VERB bjmsr-311 332 45 deviate deviate VERB bjmsr-311 332 46 yi yi PROPN bjmsr-311 332 47 s2 s2 PROPN bjmsr-311 332 48 and and CCONJ bjmsr-311 332 49 xji xji PROPN bjmsr-311 332 50 s2 s2 PROPN bjmsr-311 332 51 from from ADP bjmsr-311 332 52 k3th k3th PROPN bjmsr-311 332 53 observation observation NOUN bjmsr-311 332 54 , , PUNCT bjmsr-311 332 55 yi yi PROPN bjmsr-311 332 56 k3 k3 VERB bjmsr-311 332 57 = = PROPN bjmsr-311 332 58 yi yi PROPN bjmsr-311 332 59 s2 s2 PROPN bjmsr-311 332 60 -yk3 -yk3 PUNCT bjmsr-311 332 61 s2 s2 PROPN bjmsr-311 332 62 i=1, i=1, NOUN bjmsr-311 332 63 ... ... PUNCT bjmsr-311 332 64 ,n ,n PUNCT bjmsr-311 332 65 ( ( PUNCT bjmsr-311 332 66 79 79 NUM bjmsr-311 332 67 ) ) PUNCT bjmsr-311 332 68 xji xji PROPN bjmsr-311 333 1 k3 k3 VERB bjmsr-311 333 2 = = SYM bjmsr-311 333 3 xji xji PROPN bjmsr-311 333 4 s2 s2 PROPN bjmsr-311 333 5 xjk3 xjk3 PROPN bjmsr-311 333 6 s2 s2 PROPN bjmsr-311 333 7 i=1, i=1, PROPN bjmsr-311 333 8 ... ... PUNCT bjmsr-311 333 9 ,n ,n NOUN bjmsr-311 333 10 , , PUNCT bjmsr-311 333 11 j=3 j=3 PROPN bjmsr-311 333 12 ( ( PUNCT bjmsr-311 333 13 80 80 NUM bjmsr-311 333 14 ) ) PUNCT bjmsr-311 333 15 rewrite rewrite VERB bjmsr-311 333 16 the the DET bjmsr-311 333 17 objective objective ADJ bjmsr-311 333 18 function function NOUN bjmsr-311 333 19 as as ADP bjmsr-311 333 20 , , PUNCT bjmsr-311 333 21 n n PRON bjmsr-311 334 1 sk1k2 sk1k2 PROPN bjmsr-311 334 2 = = PROPN bjmsr-311 334 3 σ σ PROPN bjmsr-311 334 4 │ │ PROPN bjmsr-311 334 5 x1i x1i PROPN bjmsr-311 334 6 k1x2i k1x2i PUNCT bjmsr-311 334 7 k2x3i k2x3i X bjmsr-311 334 8 k3 k3 VERB bjmsr-311 334 9 │ │ ADJ bjmsr-311 334 10 │ │ ADJ bjmsr-311 334 11 yi yi NOUN bjmsr-311 334 12 s3 s3 PROPN bjmsr-311 334 13 - - PUNCT bjmsr-311 334 14 ß3x3i ß3x3i X bjmsr-311 334 15 k3 k3 PROPN bjmsr-311 334 16 │ │ X bjmsr-311 334 17 ( ( PUNCT bjmsr-311 334 18 81 81 NUM bjmsr-311 334 19 ) ) PUNCT bjmsr-311 334 20 i=1 i=1 PROPN bjmsr-311 335 1 divide divide VERB bjmsr-311 335 2 yi yi NOUN bjmsr-311 335 3 k3 k3 VERB bjmsr-311 335 4 by by ADP bjmsr-311 335 5 x3i x3i PROPN bjmsr-311 335 6 k3 k3 PROPN bjmsr-311 335 7 for for ADP bjmsr-311 335 8 all all DET bjmsr-311 335 9 i=1, i=1, NOUN bjmsr-311 335 10 ... ... PUNCT bjmsr-311 335 11 ,n ,n NOUN bjmsr-311 335 12 ; ; PUNCT bjmsr-311 335 13 yi yi PROPN bjmsr-311 335 14 s3 s3 PROPN bjmsr-311 335 15 = = PROPN bjmsr-311 335 16 yi yi PROPN bjmsr-311 335 17 k3 k3 PROPN bjmsr-311 335 18 / / SYM bjmsr-311 335 19 x3i x3i PROPN bjmsr-311 336 1 k3 k3 PROPN bjmsr-311 336 2 i=1, i=1, PROPN bjmsr-311 336 3 ... ... PUNCT bjmsr-311 336 4 ,n ,n PUNCT bjmsr-311 336 5 ( ( PUNCT bjmsr-311 336 6 82 82 NUM bjmsr-311 336 7 ) ) PUNCT bjmsr-311 336 8 finally finally ADV bjmsr-311 336 9 the the DET bjmsr-311 336 10 objective objective ADJ bjmsr-311 336 11 function function NOUN bjmsr-311 336 12 becomes become VERB bjmsr-311 336 13 , , PUNCT bjmsr-311 336 14 n n CCONJ bjmsr-311 336 15 sk1k2k3 sk1k2k3 PROPN bjmsr-311 336 16 = = PROPN bjmsr-311 336 17 σ σ PROPN bjmsr-311 336 18 │ │ PROPN bjmsr-311 336 19 x1i x1i PROPN bjmsr-311 336 20 k1x2i k1x2i PUNCT bjmsr-311 336 21 k2x3i k2x3i X bjmsr-311 336 22 k3 k3 VERB bjmsr-311 336 23 │ │ ADJ bjmsr-311 336 24 │ │ ADJ bjmsr-311 336 25 yi yi NOUN bjmsr-311 336 26 s3 s3 PROPN bjmsr-311 336 27 - - PUNCT bjmsr-311 336 28 ß3 ß3 NOUN bjmsr-311 336 29 │ │ X bjmsr-311 336 30 ( ( PUNCT bjmsr-311 336 31 83 83 NUM bjmsr-311 336 32 ) ) PUNCT bjmsr-311 336 33 i=1 i=1 PROPN bjmsr-311 336 34 rewrite rewrite PROPN bjmsr-311 336 35 ( ( PUNCT bjmsr-311 336 36 83 83 NUM bjmsr-311 336 37 ) ) PUNCT bjmsr-311 336 38 as as ADP bjmsr-311 336 39 , , PUNCT bjmsr-311 336 40 n n CCONJ bjmsr-311 336 41 sk1k2k3 sk1k2k3 PROPN bjmsr-311 336 42 = = PROPN bjmsr-311 336 43 σ σ PROPN bjmsr-311 336 44 │ │ PROPN bjmsr-311 336 45 wi wi PROPN bjmsr-311 336 46 k1k2k3 k1k2k3 PROPN bjmsr-311 336 47 │ │ X bjmsr-311 336 48 │ │ NOUN bjmsr-311 336 49 ri ri PRON bjmsr-311 336 50 s1s2s3 s1s2s3 NOUN bjmsr-311 336 51 - - PUNCT bjmsr-311 336 52 ß3 ß3 NOUN bjmsr-311 336 53 │ │ X bjmsr-311 336 54 ( ( PUNCT bjmsr-311 336 55 84 84 NUM bjmsr-311 336 56 ) ) PUNCT bjmsr-311 336 57 i=1 i=1 VERB bjmsr-311 337 1 where where SCONJ bjmsr-311 337 2 , , PUNCT bjmsr-311 337 3 wi wi PROPN bjmsr-311 337 4 k1k2k3 k1k2k3 PROPN bjmsr-311 337 5 = = SYM bjmsr-311 337 6 x1i x1i PROPN bjmsr-311 337 7 k1x2i k1x2i PUNCT bjmsr-311 337 8 k2x3i k2x3i X bjmsr-311 337 9 k3 k3 X bjmsr-311 337 10 ( ( PUNCT bjmsr-311 337 11 85 85 NUM bjmsr-311 337 12 ) ) PUNCT bjmsr-311 337 13 ri ri NOUN bjmsr-311 337 14 s1s2s3 s1s2s3 NOUN bjmsr-311 337 15 = = SYM bjmsr-311 337 16 yi yi PROPN bjmsr-311 337 17 s3 s3 PROPN bjmsr-311 337 18 ( ( PUNCT bjmsr-311 337 19 86 86 NUM bjmsr-311 337 20 ) ) PUNCT bjmsr-311 337 21 the the DET bjmsr-311 337 22 objective objective ADJ bjmsr-311 337 23 function function NOUN bjmsr-311 337 24 ( ( PUNCT bjmsr-311 337 25 84 84 NUM bjmsr-311 337 26 ) ) PUNCT bjmsr-311 337 27 is be AUX bjmsr-311 337 28 a a DET bjmsr-311 337 29 weighted weight VERB bjmsr-311 337 30 median median ADJ bjmsr-311 337 31 problem problem NOUN bjmsr-311 337 32 which which PRON bjmsr-311 337 33 may may AUX bjmsr-311 337 34 easily easily ADV bjmsr-311 337 35 be be AUX bjmsr-311 337 36 minimized minimize VERB bjmsr-311 337 37 to to PART bjmsr-311 337 38 find find VERB bjmsr-311 337 39 ß3 ß3 NOUN bjmsr-311 337 40 . . PUNCT bjmsr-311 338 1 equation equation NOUN bjmsr-311 338 2 ( ( PUNCT bjmsr-311 338 3 84 84 NUM bjmsr-311 338 4 ) ) PUNCT bjmsr-311 338 5 for for ADP bjmsr-311 338 6 the the DET bjmsr-311 338 7 general general ADJ bjmsr-311 338 8 m m PROPN bjmsr-311 338 9 parameters parameters PROPN bjmsr-311 338 10 model model PROPN bjmsr-311 338 11 m-1 m-1 PROPN bjmsr-311 338 12 yi yi PROPN bjmsr-311 338 13 = = PROPN bjmsr-311 338 14 σ σ PROPN bjmsr-311 338 15 xjißj xjißj PROPN bjmsr-311 338 16 + + CCONJ bjmsr-311 338 17 ui ui PROPN bjmsr-311 338 18 i=1, i=1, PROPN bjmsr-311 338 19 ... ... PUNCT bjmsr-311 338 20 ,n ,n PUNCT bjmsr-311 338 21 ( ( PUNCT bjmsr-311 338 22 87 87 NUM bjmsr-311 338 23 ) ) PUNCT bjmsr-311 338 24 j=0 j=0 PROPN bjmsr-311 338 25 x0i=1 x0i=1 PROPN bjmsr-311 339 1 i=1, i=1, PROPN bjmsr-311 339 2 ... ... PUNCT bjmsr-311 339 3 ,n ,n PUNCT bjmsr-311 339 4 ( ( PUNCT bjmsr-311 339 5 88 88 NUM bjmsr-311 339 6 ) ) PUNCT bjmsr-311 339 7 with with ADP bjmsr-311 339 8 the the DET bjmsr-311 339 9 corresponding correspond VERB bjmsr-311 339 10 objective objective ADJ bjmsr-311 339 11 function function NOUN bjmsr-311 339 12 , , PUNCT bjmsr-311 339 13 n n PROPN bjmsr-311 339 14 m-1 m-1 NUM bjmsr-311 339 15 s s PART bjmsr-311 339 16 = = PROPN bjmsr-311 339 17 σ σ PROPN bjmsr-311 339 18 │ │ NOUN bjmsr-311 339 19 yi yi PROPN bjmsr-311 339 20 σ σ PROPN bjmsr-311 339 21 xjißj xjißj PROPN bjmsr-311 339 22 │ │ X bjmsr-311 339 23 ( ( PUNCT bjmsr-311 339 24 89 89 NUM bjmsr-311 339 25 ) ) PUNCT bjmsr-311 339 26 i=1 i=1 PROPN bjmsr-311 339 27 j=0 j=0 PROPN bjmsr-311 339 28 is be AUX bjmsr-311 339 29 , , PUNCT bjmsr-311 339 30 n n PRON bjmsr-311 339 31 sk1k2 sk1k2 PROPN bjmsr-311 339 32 ... ... PUNCT bjmsr-311 339 33 k(m-1 k(m-1 X bjmsr-311 339 34 ) ) PUNCT bjmsr-311 340 1 = = SYM bjmsr-311 340 2 σ σ PROPN bjmsr-311 340 3 │ │ PROPN bjmsr-311 340 4 wi wi PROPN bjmsr-311 340 5 k1k2 k1k2 PROPN bjmsr-311 340 6 ... ... PUNCT bjmsr-311 340 7 k(m-1) k(m-1) PROPN bjmsr-311 340 8 │ │ ADJ bjmsr-311 340 9 │ │ NOUN bjmsr-311 340 10 ri ri NOUN bjmsr-311 340 11 s1s2 s1s2 NOUN bjmsr-311 340 12 ... ... PUNCT bjmsr-311 340 13 s(m-1)-ßm-1 s(m-1)-ßm-1 PROPN bjmsr-311 340 14 │ │ X bjmsr-311 340 15 ( ( PUNCT bjmsr-311 340 16 90 90 NUM bjmsr-311 340 17 ) ) PUNCT bjmsr-311 340 18 i=1 i=1 PROPN bjmsr-311 341 1 copyright copyright NOUN bjmsr-311 341 2 © © PROPN bjmsr-311 341 3 cc cc PROPN bjmsr-311 341 4 - - PUNCT bjmsr-311 341 5 by by ADP bjmsr-311 341 6 - - PUNCT bjmsr-311 341 7 nc nc PROPN bjmsr-311 341 8 2019 2019 NUM bjmsr-311 341 9 , , PUNCT bjmsr-311 341 10 bjmsr bjmsr PROPN bjmsr-311 341 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 342 1 bangladesh bangladesh PROPN bjmsr-311 342 2 journal journal PROPN bjmsr-311 342 3 of of ADP bjmsr-311 342 4 multidisciplinary multidisciplinary ADJ bjmsr-311 342 5 scientific scientific ADJ bjmsr-311 342 6 research research NOUN bjmsr-311 342 7 vol vol NOUN bjmsr-311 342 8 . . PROPN bjmsr-311 342 9 1 1 NUM bjmsr-311 342 10 , , PUNCT bjmsr-311 342 11 no no INTJ bjmsr-311 342 12 . . NOUN bjmsr-311 342 13 1 1 NUM bjmsr-311 342 14 ; ; PUNCT bjmsr-311 342 15 2019 2019 NUM bjmsr-311 342 16 13 13 NUM bjmsr-311 342 17 where where SCONJ bjmsr-311 342 18 , , PUNCT bjmsr-311 342 19 wi wi PROPN bjmsr-311 342 20 k1k2 k1k2 PROPN bjmsr-311 342 21 ... ... PUNCT bjmsr-311 342 22 k(m-1 k(m-1 X bjmsr-311 342 23 ) ) PUNCT bjmsr-311 342 24 = = PUNCT bjmsr-311 343 1 │ │ PROPN bjmsr-311 343 2 x1i x1i PROPN bjmsr-311 343 3 k1x2i k1x2i PUNCT bjmsr-311 343 4 k2 k2 PROPN bjmsr-311 343 5 ... ... PUNCT bjmsr-311 343 6 x(m-1)i x(m-1)i PROPN bjmsr-311 343 7 k(m-1 k(m-1 PROPN bjmsr-311 343 8 ) ) PUNCT bjmsr-311 343 9 │ │ X bjmsr-311 343 10 ( ( PUNCT bjmsr-311 343 11 91 91 NUM bjmsr-311 343 12 ) ) PUNCT bjmsr-311 343 13 ri ri NOUN bjmsr-311 343 14 s1s2 s1s2 PROPN bjmsr-311 343 15 ... ... PUNCT bjmsr-311 343 16 s(m-1 s(m-1 PROPN bjmsr-311 343 17 ) ) PUNCT bjmsr-311 343 18 = = PROPN bjmsr-311 343 19 yi yi PROPN bjmsr-311 343 20 s(m-1 s(m-1 PROPN bjmsr-311 343 21 ) ) PUNCT bjmsr-311 343 22 ( ( PUNCT bjmsr-311 343 23 92 92 NUM bjmsr-311 343 24 ) ) PUNCT bjmsr-311 343 25 now now ADV bjmsr-311 343 26 , , PUNCT bjmsr-311 343 27 we we PRON bjmsr-311 343 28 proceed proceed VERB bjmsr-311 343 29 to to PART bjmsr-311 343 30 explain explain VERB bjmsr-311 343 31 the the DET bjmsr-311 343 32 properties property NOUN bjmsr-311 343 33 of of ADP bjmsr-311 343 34 algorithm algorithm NOUN bjmsr-311 343 35 4 4 NUM bjmsr-311 343 36 by by ADP bjmsr-311 343 37 using use VERB bjmsr-311 343 38 the the DET bjmsr-311 343 39 formulation formulation NOUN bjmsr-311 343 40 described describe VERB bjmsr-311 343 41 above above ADV bjmsr-311 343 42 . . PUNCT bjmsr-311 344 1 property property NOUN bjmsr-311 344 2 1 1 NUM bjmsr-311 344 3 if if SCONJ bjmsr-311 344 4 we we PRON bjmsr-311 344 5 start start VERB bjmsr-311 344 6 the the DET bjmsr-311 344 7 computation computation NOUN bjmsr-311 344 8 with with ADP bjmsr-311 344 9 m-1 m-1 PROPN bjmsr-311 344 10 points point NOUN bjmsr-311 344 11 which which PRON bjmsr-311 344 12 do do AUX bjmsr-311 344 13 not not PART bjmsr-311 344 14 belong belong VERB bjmsr-311 344 15 to to ADP bjmsr-311 344 16 the the DET bjmsr-311 344 17 original original ADJ bjmsr-311 344 18 set set NOUN bjmsr-311 344 19 of of ADP bjmsr-311 344 20 observations observation NOUN bjmsr-311 344 21 , , PUNCT bjmsr-311 344 22 the the DET bjmsr-311 344 23 value value NOUN bjmsr-311 344 24 of of ADP bjmsr-311 344 25 s s NOUN bjmsr-311 344 26 decreases decrease NOUN bjmsr-311 344 27 to to ADP bjmsr-311 344 28 its its PRON bjmsr-311 344 29 global global ADJ bjmsr-311 344 30 minimum minimum NOUN bjmsr-311 344 31 at at ADP bjmsr-311 344 32 each each DET bjmsr-311 344 33 iteration iteration NOUN bjmsr-311 344 34 . . PUNCT bjmsr-311 345 1 suppose suppose VERB bjmsr-311 345 2 the the DET bjmsr-311 345 3 points point NOUN bjmsr-311 345 4 ( ( PUNCT bjmsr-311 345 5 yn+1, yn+1, PROPN bjmsr-311 345 6 ... ... PUNCT bjmsr-311 345 7 ,xm-1,n+1), ,xm-1,n+1), PROPN bjmsr-311 345 8 ... ... PUNCT bjmsr-311 345 9 ,(yn+m-1, ,(yn+m-1, NOUN bjmsr-311 345 10 ... ... PUNCT bjmsr-311 345 11 ,xm-1,n+m-1 ,xm-1,n+m-1 PUNCT bjmsr-311 345 12 ) ) PUNCT bjmsr-311 345 13 do do AUX bjmsr-311 345 14 not not PART bjmsr-311 345 15 belong belong VERB bjmsr-311 345 16 to to ADP bjmsr-311 345 17 our our PRON bjmsr-311 345 18 sample sample NOUN bjmsr-311 345 19 points point NOUN bjmsr-311 345 20 . . PUNCT bjmsr-311 346 1 if if SCONJ bjmsr-311 346 2 n+1,n+2, n+1,n+2, PROPN bjmsr-311 346 3 ... ... PUNCT bjmsr-311 346 4 ,n+m-1 ,n+m-1 PUNCT bjmsr-311 346 5 are be AUX bjmsr-311 346 6 assigned assign VERB bjmsr-311 346 7 to to ADP bjmsr-311 346 8 k1,k2, k1,k2, NOUN bjmsr-311 346 9 ... ... PUNCT bjmsr-311 346 10 ,k(m-1 ,k(m-1 PROPN bjmsr-311 346 11 ) ) PUNCT bjmsr-311 346 12 , , PUNCT bjmsr-311 346 13 then then ADV bjmsr-311 346 14 minimizing minimize VERB bjmsr-311 346 15 the the DET bjmsr-311 346 16 function function NOUN bjmsr-311 346 17 in in ADP bjmsr-311 346 18 ( ( PUNCT bjmsr-311 346 19 90 90 NUM bjmsr-311 346 20 ) ) PUNCT bjmsr-311 346 21 leads lead VERB bjmsr-311 346 22 to to ADP bjmsr-311 346 23 finding find VERB bjmsr-311 346 24 a a DET bjmsr-311 346 25 new new ADJ bjmsr-311 346 26 point point NOUN bjmsr-311 346 27 m m VERB bjmsr-311 346 28 which which PRON bjmsr-311 346 29 belongs belong VERB bjmsr-311 346 30 to to ADP bjmsr-311 346 31 the the DET bjmsr-311 346 32 sample sample NOUN bjmsr-311 346 33 observations observation NOUN bjmsr-311 346 34 . . PUNCT bjmsr-311 347 1 replacing replace VERB bjmsr-311 347 2 k1 k1 NOUN bjmsr-311 347 3 by by ADP bjmsr-311 347 4 m m NOUN bjmsr-311 347 5 and and CCONJ bjmsr-311 347 6 deleting delete VERB bjmsr-311 347 7 the the DET bjmsr-311 347 8 ( ( PUNCT bjmsr-311 347 9 n+1)th n+1)th NOUN bjmsr-311 347 10 point point NOUN bjmsr-311 347 11 from from ADP bjmsr-311 347 12 the the DET bjmsr-311 347 13 basis basis NOUN bjmsr-311 347 14 and and CCONJ bjmsr-311 347 15 minimizing minimize VERB bjmsr-311 347 16 ( ( PUNCT bjmsr-311 347 17 90 90 NUM bjmsr-311 347 18 ) ) PUNCT bjmsr-311 347 19 leads lead VERB bjmsr-311 347 20 to to ADP bjmsr-311 347 21 finding find VERB bjmsr-311 347 22 another another DET bjmsr-311 347 23 point point NOUN bjmsr-311 347 24 m m NOUN bjmsr-311 347 25 ' ' PUNCT bjmsr-311 347 26 in in ADP bjmsr-311 347 27 the the DET bjmsr-311 347 28 sample sample NOUN bjmsr-311 347 29 which which PRON bjmsr-311 347 30 will will AUX bjmsr-311 347 31 be be AUX bjmsr-311 347 32 replaced replace VERB bjmsr-311 347 33 by by ADP bjmsr-311 347 34 the the DET bjmsr-311 347 35 k2 k2 PROPN bjmsr-311 347 36 th th NUM bjmsr-311 347 37 observation observation NOUN bjmsr-311 347 38 which which PRON bjmsr-311 347 39 is be AUX bjmsr-311 347 40 out out ADP bjmsr-311 347 41 of of ADP bjmsr-311 347 42 our our PRON bjmsr-311 347 43 sample sample NOUN bjmsr-311 347 44 . . PUNCT bjmsr-311 348 1 thus thus ADV bjmsr-311 348 2 , , PUNCT bjmsr-311 348 3 in in ADP bjmsr-311 348 4 each each DET bjmsr-311 348 5 iteration iteration NOUN bjmsr-311 348 6 one one NUM bjmsr-311 348 7 of of ADP bjmsr-311 348 8 the the DET bjmsr-311 348 9 out out ADP bjmsr-311 348 10 of of ADP bjmsr-311 348 11 sample sample NOUN bjmsr-311 348 12 points point NOUN bjmsr-311 348 13 is be AUX bjmsr-311 348 14 deleted delete VERB bjmsr-311 348 15 , , PUNCT bjmsr-311 348 16 and and CCONJ bjmsr-311 348 17 optimization optimization NOUN bjmsr-311 348 18 procedure procedure NOUN bjmsr-311 348 19 will will AUX bjmsr-311 348 20 be be AUX bjmsr-311 348 21 done do VERB bjmsr-311 348 22 on on ADP bjmsr-311 348 23 the the DET bjmsr-311 348 24 sample sample NOUN bjmsr-311 348 25 points point NOUN bjmsr-311 348 26 after after ADP bjmsr-311 348 27 m-1 m-1 PROPN bjmsr-311 348 28 iterations iteration NOUN bjmsr-311 348 29 . . PUNCT bjmsr-311 349 1 this this DET bjmsr-311 349 2 property property NOUN bjmsr-311 349 3 has have VERB bjmsr-311 349 4 a a DET bjmsr-311 349 5 good good ADJ bjmsr-311 349 6 performance performance NOUN bjmsr-311 349 7 on on ADP bjmsr-311 349 8 ill ill ADV bjmsr-311 349 9 - - PUNCT bjmsr-311 349 10 conditioned condition VERB bjmsr-311 349 11 data datum NOUN bjmsr-311 349 12 . . PUNCT bjmsr-311 350 1 that that PRON bjmsr-311 350 2 is be AUX bjmsr-311 350 3 if if SCONJ bjmsr-311 350 4 for for ADP bjmsr-311 350 5 example example NOUN bjmsr-311 350 6 , , PUNCT bjmsr-311 350 7 rounding round VERB bjmsr-311 350 8 error error NOUN bjmsr-311 350 9 causes cause VERB bjmsr-311 350 10 an an DET bjmsr-311 350 11 observation observation NOUN bjmsr-311 350 12 to to PART bjmsr-311 350 13 get get VERB bjmsr-311 350 14 incorrect incorrect ADJ bjmsr-311 350 15 rounded rounded ADJ bjmsr-311 350 16 value value NOUN bjmsr-311 350 17 , , PUNCT bjmsr-311 350 18 then then ADV bjmsr-311 350 19 this this DET bjmsr-311 350 20 point point NOUN bjmsr-311 350 21 in in ADP bjmsr-311 350 22 the the DET bjmsr-311 350 23 next next ADJ bjmsr-311 350 24 iteration iteration NOUN bjmsr-311 350 25 will will AUX bjmsr-311 350 26 be be AUX bjmsr-311 350 27 replaced replace VERB bjmsr-311 350 28 by by ADP bjmsr-311 350 29 a a DET bjmsr-311 350 30 sample sample NOUN bjmsr-311 350 31 point point NOUN bjmsr-311 350 32 and and CCONJ bjmsr-311 350 33 thus thus ADV bjmsr-311 350 34 redirect redirect VERB bjmsr-311 350 35 the the DET bjmsr-311 350 36 path path NOUN bjmsr-311 350 37 of of ADP bjmsr-311 350 38 descending descend VERB bjmsr-311 350 39 to to ADP bjmsr-311 350 40 the the DET bjmsr-311 350 41 right right ADJ bjmsr-311 350 42 points point NOUN bjmsr-311 350 43 . . PUNCT bjmsr-311 351 1 property property NOUN bjmsr-311 351 2 2 2 NUM bjmsr-311 351 3 reduction reduction NOUN bjmsr-311 351 4 of of ADP bjmsr-311 351 5 m-1 m-1 PROPN bjmsr-311 351 6 parameters parameter NOUN bjmsr-311 351 7 model model VERB bjmsr-311 351 8 to to ADP bjmsr-311 351 9 fewer few ADJ bjmsr-311 351 10 parameters parameter NOUN bjmsr-311 351 11 model model NOUN bjmsr-311 351 12 can can AUX bjmsr-311 351 13 be be AUX bjmsr-311 351 14 made make VERB bjmsr-311 351 15 by by ADP bjmsr-311 351 16 using use VERB bjmsr-311 351 17 the the DET bjmsr-311 351 18 computation computation NOUN bjmsr-311 351 19 of of ADP bjmsr-311 351 20 m-1 m-1 PROPN bjmsr-311 351 21 parameters parameter NOUN bjmsr-311 351 22 model model NOUN bjmsr-311 351 23 and and CCONJ bjmsr-311 351 24 conversely conversely ADV bjmsr-311 351 25 . . PUNCT bjmsr-311 352 1 thus thus ADV bjmsr-311 352 2 stepwise stepwise NOUN bjmsr-311 352 3 and and CCONJ bjmsr-311 352 4 all all DET bjmsr-311 352 5 possible possible ADJ bjmsr-311 352 6 regressions regression NOUN bjmsr-311 352 7 may may AUX bjmsr-311 352 8 be be AUX bjmsr-311 352 9 computed compute VERB bjmsr-311 352 10 efficiently efficiently ADV bjmsr-311 352 11 . . PUNCT bjmsr-311 353 1 to to PART bjmsr-311 353 2 show show VERB bjmsr-311 353 3 this this DET bjmsr-311 353 4 property property NOUN bjmsr-311 353 5 , , PUNCT bjmsr-311 353 6 let let VERB bjmsr-311 353 7 us we PRON bjmsr-311 353 8 deal deal VERB bjmsr-311 353 9 with with ADP bjmsr-311 353 10 equation equation NOUN bjmsr-311 353 11 ( ( PUNCT bjmsr-311 353 12 86 86 NUM bjmsr-311 353 13 ) ) PUNCT bjmsr-311 353 14 . . PUNCT bjmsr-311 354 1 value value NOUN bjmsr-311 354 2 of of ADP bjmsr-311 354 3 ri ri PROPN bjmsr-311 354 4 s1s2s3 s1s2s3 PROPN bjmsr-311 354 5 may may AUX bjmsr-311 354 6 be be AUX bjmsr-311 354 7 computed compute VERB bjmsr-311 354 8 by by ADP bjmsr-311 354 9 substituting substitute VERB bjmsr-311 354 10 ( ( PUNCT bjmsr-311 354 11 67 67 NUM bjmsr-311 354 12 ) ) PUNCT bjmsr-311 354 13 , , PUNCT bjmsr-311 354 14 ( ( PUNCT bjmsr-311 354 15 68 68 NUM bjmsr-311 354 16 ) ) PUNCT bjmsr-311 354 17 , , PUNCT bjmsr-311 354 18 ( ( PUNCT bjmsr-311 354 19 70 70 NUM bjmsr-311 354 20 ) ) PUNCT bjmsr-311 354 21 , , PUNCT bjmsr-311 354 22 ( ( PUNCT bjmsr-311 354 23 71 71 NUM bjmsr-311 354 24 ) ) PUNCT bjmsr-311 354 25 , , PUNCT bjmsr-311 354 26 ( ( PUNCT bjmsr-311 354 27 73 73 NUM bjmsr-311 354 28 ) ) PUNCT bjmsr-311 354 29 , , PUNCT bjmsr-311 354 30 ( ( PUNCT bjmsr-311 354 31 74 74 NUM bjmsr-311 354 32 ) ) PUNCT bjmsr-311 354 33 , , PUNCT bjmsr-311 354 34 ( ( PUNCT bjmsr-311 354 35 76 76 NUM bjmsr-311 354 36 ) ) PUNCT bjmsr-311 354 37 , , PUNCT bjmsr-311 354 38 ( ( PUNCT bjmsr-311 354 39 77 77 NUM bjmsr-311 354 40 ) ) PUNCT bjmsr-311 354 41 , , PUNCT bjmsr-311 354 42 ( ( PUNCT bjmsr-311 354 43 79 79 NUM bjmsr-311 354 44 ) ) PUNCT bjmsr-311 354 45 , , PUNCT bjmsr-311 354 46 ( ( PUNCT bjmsr-311 354 47 80 80 NUM bjmsr-311 354 48 ) ) PUNCT bjmsr-311 354 49 and and CCONJ bjmsr-311 354 50 ( ( PUNCT bjmsr-311 354 51 82 82 NUM bjmsr-311 354 52 ) ) PUNCT bjmsr-311 354 53 into into ADP bjmsr-311 354 54 ( ( PUNCT bjmsr-311 354 55 86 86 NUM bjmsr-311 354 56 ) ) PUNCT bjmsr-311 354 57 . . PUNCT bjmsr-311 355 1 the the DET bjmsr-311 355 2 result result NOUN bjmsr-311 355 3 is be AUX bjmsr-311 355 4 , , PUNCT bjmsr-311 355 5 1 1 NUM bjmsr-311 355 6 2 2 NUM bjmsr-311 355 7 1 1 NUM bjmsr-311 355 8 3 3 NUM bjmsr-311 355 9 1 1 NUM bjmsr-311 355 10 2 2 NUM bjmsr-311 355 11 1 1 NUM bjmsr-311 355 12 1 1 NUM bjmsr-311 355 13 1 1 NUM bjmsr-311 355 14 1 1 NUM bjmsr-311 355 15 1 1 NUM bjmsr-311 355 16 2 2 NUM bjmsr-311 355 17 1 1 NUM bjmsr-311 355 18 1 1 NUM bjmsr-311 355 19 1 1 NUM bjmsr-311 355 20 3 3 NUM bjmsr-311 355 21 1 1 NUM bjmsr-311 355 22 1 1 NUM bjmsr-311 355 23 1 1 NUM bjmsr-311 355 24 2 2 NUM bjmsr-311 355 25 1 1 NUM bjmsr-311 355 26 1 1 NUM bjmsr-311 355 27 2 2 NUM bjmsr-311 355 28 2 2 NUM bjmsr-311 355 29 1 1 NUM bjmsr-311 355 30 2 2 NUM bjmsr-311 355 31 2 2 NUM bjmsr-311 355 32 2 2 NUM bjmsr-311 355 33 1 1 NUM bjmsr-311 355 34 2 2 NUM bjmsr-311 355 35 3 3 NUM bjmsr-311 355 36 2 2 NUM bjmsr-311 355 37 1 1 NUM bjmsr-311 355 38 2 2 NUM bjmsr-311 355 39 2 2 NUM bjmsr-311 355 40 2 2 NUM bjmsr-311 355 41 1 1 NUM bjmsr-311 355 42 1 1 NUM bjmsr-311 355 43 1 1 NUM bjmsr-311 355 44 1 1 NUM bjmsr-311 355 45 1 1 NUM bjmsr-311 355 46 2 2 NUM bjmsr-311 355 47 1 1 NUM bjmsr-311 355 48 1 1 NUM bjmsr-311 355 49 1 1 NUM bjmsr-311 355 50 3 3 NUM bjmsr-311 355 51 1 1 NUM bjmsr-311 355 52 1 1 NUM bjmsr-311 355 53 1 1 NUM bjmsr-311 355 54 2 2 NUM bjmsr-311 355 55 1 1 NUM bjmsr-311 355 56 11 11 NUM bjmsr-311 355 57 2 2 NUM bjmsr-311 355 58 3 3 NUM bjmsr-311 355 59 3 3 NUM bjmsr-311 355 60 3 3 NUM bjmsr-311 355 61 1 1 NUM bjmsr-311 355 62 3 3 NUM bjmsr-311 355 63 2 2 NUM bjmsr-311 355 64 3 3 NUM bjmsr-311 355 65 1 1 NUM bjmsr-311 355 66 1 1 NUM bjmsr-311 355 67 1 1 NUM bjmsr-311 355 68 1 1 NUM bjmsr-311 355 69 1 1 NUM bjmsr-311 355 70 2 2 NUM bjmsr-311 355 71 1 1 NUM bjmsr-311 355 72 1 1 NUM bjmsr-311 355 73 2 2 NUM bjmsr-311 355 74 2 2 NUM bjmsr-311 355 75 1 1 NUM bjmsr-311 355 76 2 2 NUM bjmsr-311 355 77 1 1 NUM bjmsr-311 355 78 1 1 NUM bjmsr-311 355 79 1 1 NUM bjmsr-311 356 1 i i NOUN bjmsr-311 356 2 k k PROPN bjmsr-311 357 1 k k PROPN bjmsr-311 358 1 k k PROPN bjmsr-311 359 1 k k PROPN bjmsr-311 360 1 k k PROPN bjmsr-311 361 1 k k PROPN bjmsr-311 362 1 k k PROPN bjmsr-311 363 1 i i PRON bjmsr-311 363 2 k k PROPN bjmsr-311 364 1 k k PROPN bjmsr-311 365 1 k k PROPN bjmsr-311 366 1 k k PROPN bjmsr-311 367 1 k k PROPN bjmsr-311 368 1 k k PROPN bjmsr-311 369 1 k k PROPN bjmsr-311 370 1 i i PRON bjmsr-311 370 2 k k PROPN bjmsr-311 371 1 k k PROPN bjmsr-311 372 1 k k PROPN bjmsr-311 373 1 k k PROPN bjmsr-311 374 1 k k PROPN bjmsr-311 375 1 k k PROPN bjmsr-311 376 1 k k PROPN bjmsr-311 377 1 i i PRON bjmsr-311 377 2 k k PROPN bjmsr-311 378 1 k k PROPN bjmsr-311 378 2 k k PROPN bjmsr-311 378 3 k k PROPN bjmsr-311 378 4 k k PROPN bjmsr-311 378 5 k k PROPN bjmsr-311 378 6 ks ks PROPN bjmsr-311 378 7 s s X bjmsr-311 378 8 s s X bjmsr-311 379 1 i i PRON bjmsr-311 380 1 i i PRON bjmsr-311 380 2 k k PROPN bjmsr-311 381 1 k k PROPN bjmsr-311 381 2 k k PROPN bjmsr-311 382 1 i i PRON bjmsr-311 382 2 k k PROPN bjmsr-311 383 1 k k PROPN bjmsr-311 383 2 k k PROPN bjmsr-311 384 1 i i PRON bjmsr-311 384 2 k k INTJ bjmsr-311 385 1 i i PRON bjmsr-311 385 2 k k PROPN bjmsr-311 386 1 y y PROPN bjmsr-311 386 2 y y PROPN bjmsr-311 386 3 y y PROPN bjmsr-311 386 4 y y PROPN bjmsr-311 386 5 y y PROPN bjmsr-311 386 6 y y PROPN bjmsr-311 386 7 y y PROPN bjmsr-311 386 8 y y PROPN bjmsr-311 386 9 x x PUNCT bjmsr-311 387 1 x x PUNCT bjmsr-311 387 2 x x PUNCT bjmsr-311 387 3 x x PUNCT bjmsr-311 387 4 x x PUNCT bjmsr-311 387 5 x x PUNCT bjmsr-311 387 6 x x PUNCT bjmsr-311 387 7 x x PUNCT bjmsr-311 387 8 x x PUNCT bjmsr-311 387 9 x x PUNCT bjmsr-311 387 10 x x PUNCT bjmsr-311 387 11 x x PUNCT bjmsr-311 387 12 x x PUNCT bjmsr-311 387 13 x x PUNCT bjmsr-311 387 14 x x PUNCT bjmsr-311 387 15 x x PUNCT bjmsr-311 387 16 x x PUNCT bjmsr-311 387 17 x x PUNCT bjmsr-311 387 18 x x PUNCT bjmsr-311 387 19 x x PUNCT bjmsr-311 387 20 x x PUNCT bjmsr-311 387 21 x x PUNCT bjmsr-311 387 22 x x PUNCT bjmsr-311 387 23 x x PUNCT bjmsr-311 387 24 r r NOUN bjmsr-311 387 25 x x NOUN bjmsr-311 387 26 x x PUNCT bjmsr-311 387 27 x x PUNCT bjmsr-311 387 28 x x PUNCT bjmsr-311 387 29 x x PUNCT bjmsr-311 387 30 x x PUNCT bjmsr-311 387 31 x x PUNCT bjmsr-311 387 32 x x PUNCT bjmsr-311 387 33 x x PUNCT bjmsr-311 387 34 x x PUNCT bjmsr-311 387 35 x x SYM bjmsr-311 387 36 x x PUNCT bjmsr-311 387 37 x x SYM bjmsr-311 387 38   PROPN bjmsr-311 387 39   PROPN bjmsr-311 387 40   NOUN bjmsr-311 387 41   PUNCT bjmsr-311 387 42   PROPN bjmsr-311 387 43   PROPN bjmsr-311 387 44   PROPN bjmsr-311 387 45   PROPN bjmsr-311 387 46   PROPN bjmsr-311 387 47   PROPN bjmsr-311 387 48   PROPN bjmsr-311 387 49   PROPN bjmsr-311 387 50   PROPN bjmsr-311 387 51   PROPN bjmsr-311 387 52   PROPN bjmsr-311 387 53   PROPN bjmsr-311 387 54   PROPN bjmsr-311 387 55   PROPN bjmsr-311 387 56   PROPN bjmsr-311 387 57   PROPN bjmsr-311 387 58   PROPN bjmsr-311 387 59   PROPN bjmsr-311 387 60   PROPN bjmsr-311 387 61   PROPN bjmsr-311 387 62   PROPN bjmsr-311 387 63   PROPN bjmsr-311 387 64   PROPN bjmsr-311 387 65   PROPN bjmsr-311 387 66   PROPN bjmsr-311 387 67 3 3 NUM bjmsr-311 387 68 3 3 NUM bjmsr-311 387 69 3 3 NUM bjmsr-311 387 70 1 1 NUM bjmsr-311 387 71 3 3 NUM bjmsr-311 387 72 2 2 NUM bjmsr-311 387 73 3 3 NUM bjmsr-311 387 74 1 1 NUM bjmsr-311 387 75 1 1 NUM bjmsr-311 387 76 3 3 NUM bjmsr-311 387 77 1 1 NUM bjmsr-311 387 78 1 1 NUM bjmsr-311 387 79 1 1 NUM bjmsr-311 387 80 2 2 NUM bjmsr-311 387 81 1 1 NUM bjmsr-311 387 82 1 1 NUM bjmsr-311 387 83 2 2 NUM bjmsr-311 387 84 2 2 NUM bjmsr-311 387 85 1 1 NUM bjmsr-311 387 86 2 2 NUM bjmsr-311 387 87 3 3 NUM bjmsr-311 387 88 2 2 NUM bjmsr-311 387 89 1 1 NUM bjmsr-311 387 90 2 2 NUM bjmsr-311 387 91 2 2 NUM bjmsr-311 387 92 2 2 NUM bjmsr-311 387 93 1 1 NUM bjmsr-311 387 94 1 1 NUM bjmsr-311 387 95 2 2 NUM bjmsr-311 387 96 1 1 NUM bjmsr-311 387 97 1 1 NUM bjmsr-311 387 98 1 1 NUM bjmsr-311 387 99 3 3 NUM bjmsr-311 387 100 1 1 NUM bjmsr-311 387 101 1 1 NUM bjmsr-311 387 102 1 1 NUM bjmsr-311 387 103 2 2 NUM bjmsr-311 387 104 1 1 NUM bjmsr-311 387 105 1 1 NUM bjmsr-311 387 106 k k NOUN bjmsr-311 387 107 k k PROPN bjmsr-311 388 1 k k PROPN bjmsr-311 388 2 k k PROPN bjmsr-311 389 1 k k PROPN bjmsr-311 389 2 k k PROPN bjmsr-311 390 1 k k PROPN bjmsr-311 390 2 k k PROPN bjmsr-311 391 1 k k PROPN bjmsr-311 391 2 k k PROPN bjmsr-311 392 1 k k PROPN bjmsr-311 392 2 k k PROPN bjmsr-311 393 1 k k PROPN bjmsr-311 393 2 k k PROPN bjmsr-311 394 1 k k PROPN bjmsr-311 394 2 k k PROPN bjmsr-311 395 1 k k PROPN bjmsr-311 396 1 k k PROPN bjmsr-311 397 1 k k PROPN bjmsr-311 397 2 k k PUNCT bjmsr-311 397 3 x x PUNCT bjmsr-311 397 4 x x PUNCT bjmsr-311 397 5 x x PUNCT bjmsr-311 397 6 x x PUNCT bjmsr-311 397 7 x x PUNCT bjmsr-311 397 8 x x PUNCT bjmsr-311 397 9 x x PUNCT bjmsr-311 397 10 x x PUNCT bjmsr-311 397 11 x x PUNCT bjmsr-311 397 12 x x PUNCT bjmsr-311 397 13 x x PUNCT bjmsr-311 397 14 x x PUNCT bjmsr-311 397 15 x x PUNCT bjmsr-311 397 16 x x PUNCT bjmsr-311 397 17 x x PUNCT bjmsr-311 397 18 x x PUNCT bjmsr-311 397 19 x x SYM bjmsr-311 397 20 x x PUNCT bjmsr-311 397 21 x x SYM bjmsr-311 397 22   PROPN bjmsr-311 397 23   PROPN bjmsr-311 397 24   PROPN bjmsr-311 397 25   PROPN bjmsr-311 397 26   PROPN bjmsr-311 397 27   PROPN bjmsr-311 397 28   PROPN bjmsr-311 397 29   PROPN bjmsr-311 397 30   PROPN bjmsr-311 397 31   PROPN bjmsr-311 397 32   PROPN bjmsr-311 397 33   PROPN bjmsr-311 397 34   NOUN bjmsr-311 397 35 ( ( PUNCT bjmsr-311 397 36 93 93 NUM bjmsr-311 397 37 ) ) PUNCT bjmsr-311 397 38 by by ADP bjmsr-311 397 39 inspection inspection NOUN bjmsr-311 397 40 , , PUNCT bjmsr-311 397 41 it it PRON bjmsr-311 397 42 is be AUX bjmsr-311 397 43 obvious obvious ADJ bjmsr-311 397 44 that that SCONJ bjmsr-311 397 45 the the DET bjmsr-311 397 46 contents content NOUN bjmsr-311 397 47 of of ADP bjmsr-311 397 48 rectangle rectangle NOUN bjmsr-311 397 49 grid grid NOUN bjmsr-311 397 50 lines line NOUN bjmsr-311 397 51 in in ADP bjmsr-311 397 52 ( ( PUNCT bjmsr-311 397 53 93 93 NUM bjmsr-311 397 54 ) ) PUNCT bjmsr-311 397 55 are be AUX bjmsr-311 397 56 ri ri PROPN bjmsr-311 397 57 s1 s1 NOUN bjmsr-311 397 58 , , PUNCT bjmsr-311 397 59 ri ri PROPN bjmsr-311 397 60 s1s2 s1s2 PROPN bjmsr-311 397 61 and and CCONJ bjmsr-311 397 62 ri ri PROPN bjmsr-311 397 63 s1s2s3 s1s2s3 PROPN bjmsr-311 397 64 . . PUNCT bjmsr-311 398 1 generally generally ADV bjmsr-311 398 2 , , PUNCT bjmsr-311 398 3 ri ri PROPN bjmsr-311 398 4 s1s2 s1s2 PROPN bjmsr-311 398 5 ... ... PUNCT bjmsr-311 398 6 s(m-1 s(m-1 PROPN bjmsr-311 398 7 ) ) PUNCT bjmsr-311 398 8 has have VERB bjmsr-311 398 9 the the DET bjmsr-311 398 10 following follow VERB bjmsr-311 398 11 scheme scheme NOUN bjmsr-311 398 12 , , PUNCT bjmsr-311 398 13 1 1 NUM bjmsr-311 398 14 1 1 NUM bjmsr-311 398 15 2 2 NUM bjmsr-311 398 16 1 1 NUM bjmsr-311 398 17 ... ... PUNCT bjmsr-311 398 18 ( ( PUNCT bjmsr-311 398 19 1 1 X bjmsr-311 398 20 ) ) SYM bjmsr-311 398 21 1 1 NUM bjmsr-311 398 22 1 1 NUM bjmsr-311 398 23 2 2 NUM bjmsr-311 398 24 ... ... PUNCT bjmsr-311 398 25 ( ( PUNCT bjmsr-311 398 26 1 1 X bjmsr-311 398 27 ) ) PUNCT bjmsr-311 398 28 s s VERB bjmsr-311 399 1 i i PRON bjmsr-311 399 2 s s VERB bjmsr-311 399 3 s s X bjmsr-311 399 4 s s X bjmsr-311 399 5 s s NOUN bjmsr-311 399 6 m m VERB bjmsr-311 399 7 i i NOUN bjmsr-311 399 8 s s VERB bjmsr-311 399 9 s s X bjmsr-311 399 10 s s NOUN bjmsr-311 399 11 m m VERB bjmsr-311 400 1 i i NOUN bjmsr-311 400 2 r r NOUN bjmsr-311 400 3 r r NOUN bjmsr-311 400 4 r r NOUN bjmsr-311 400 5 r r NOUN bjmsr-311 400 6   PROPN bjmsr-311 400 7   NOUN bjmsr-311 400 8   PRON bjmsr-311 400 9 ( ( PUNCT bjmsr-311 400 10 94 94 NUM bjmsr-311 400 11 ) ) PUNCT bjmsr-311 400 12 a a DET bjmsr-311 400 13 similar similar ADJ bjmsr-311 400 14 discussion discussion NOUN bjmsr-311 400 15 may may AUX bjmsr-311 400 16 also also ADV bjmsr-311 400 17 be be AUX bjmsr-311 400 18 performed perform VERB bjmsr-311 400 19 for for ADP bjmsr-311 400 20 wi wi PROPN bjmsr-311 400 21 k1k2 k1k2 PROPN bjmsr-311 400 22 ... ... PUNCT bjmsr-311 400 23 k(m-1 k(m-1 PROPN bjmsr-311 400 24 ) ) PUNCT bjmsr-311 400 25 . . PUNCT bjmsr-311 401 1 rewrite rewrite VERB bjmsr-311 401 2 ( ( PUNCT bjmsr-311 401 3 91 91 NUM bjmsr-311 401 4 ) ) PUNCT bjmsr-311 401 5 by by ADP bjmsr-311 401 6 substitution substitution NOUN bjmsr-311 401 7 of of ADP bjmsr-311 401 8 ( ( PUNCT bjmsr-311 401 9 68 68 NUM bjmsr-311 401 10 ) ) PUNCT bjmsr-311 401 11 , , PUNCT bjmsr-311 401 12 ( ( PUNCT bjmsr-311 401 13 74 74 NUM bjmsr-311 401 14 ) ) PUNCT bjmsr-311 401 15 and and CCONJ bjmsr-311 401 16 ( ( PUNCT bjmsr-311 401 17 80 80 NUM bjmsr-311 401 18 ) ) PUNCT bjmsr-311 401 19 in in ADP bjmsr-311 401 20 ( ( PUNCT bjmsr-311 401 21 91 91 NUM bjmsr-311 401 22 ) ) PUNCT bjmsr-311 401 23 , , PUNCT bjmsr-311 401 24 copyright copyright NOUN bjmsr-311 401 25 © © PROPN bjmsr-311 401 26 cc cc PROPN bjmsr-311 401 27 - - PUNCT bjmsr-311 401 28 by by ADP bjmsr-311 401 29 - - PUNCT bjmsr-311 401 30 nc nc PROPN bjmsr-311 401 31 2019 2019 NUM bjmsr-311 401 32 , , PUNCT bjmsr-311 401 33 bjmsr bjmsr PROPN bjmsr-311 401 34 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 402 1 bangladesh bangladesh PROPN bjmsr-311 402 2 journal journal PROPN bjmsr-311 402 3 of of ADP bjmsr-311 402 4 multidisciplinary multidisciplinary ADJ bjmsr-311 402 5 scientific scientific ADJ bjmsr-311 402 6 research research NOUN bjmsr-311 402 7 vol vol NOUN bjmsr-311 402 8 . . PROPN bjmsr-311 402 9 1 1 NUM bjmsr-311 402 10 , , PUNCT bjmsr-311 402 11 no no INTJ bjmsr-311 402 12 . . NOUN bjmsr-311 402 13 1 1 NUM bjmsr-311 402 14 ; ; PUNCT bjmsr-311 402 15 2019 2019 NUM bjmsr-311 402 16 14 14 NUM bjmsr-311 402 17   NOUN bjmsr-311 402 18   NOUN bjmsr-311 402 19 1 1 NUM bjmsr-311 402 20 2 2 NUM bjmsr-311 402 21 3 3 NUM bjmsr-311 402 22 3 3 NUM bjmsr-311 402 23 3 3 NUM bjmsr-311 402 24 3 3 NUM bjmsr-311 402 25 1 1 NUM bjmsr-311 402 26 3 3 NUM bjmsr-311 402 27 2 2 NUM bjmsr-311 402 28 3 3 NUM bjmsr-311 402 29 13 13 NUM bjmsr-311 402 30 3 3 NUM bjmsr-311 402 31 1 1 NUM bjmsr-311 402 32 3 3 NUM bjmsr-311 402 33 2 2 NUM bjmsr-311 402 34 3 3 NUM bjmsr-311 402 35 1 1 NUM bjmsr-311 402 36 2 2 NUM bjmsr-311 402 37 2 2 NUM bjmsr-311 402 38 1 1 NUM bjmsr-311 402 39 2 2 NUM bjmsr-311 402 40 2 2 NUM bjmsr-311 402 41 2 2 NUM bjmsr-311 402 42 1 1 NUM bjmsr-311 402 43 1 1 NUM bjmsr-311 402 44 3 3 NUM bjmsr-311 402 45 1 1 NUM bjmsr-311 402 46 1 1 NUM bjmsr-311 402 47 1 1 NUM bjmsr-311 402 48 2 2 NUM bjmsr-311 402 49 1 1 NUM bjmsr-311 402 50 11 11 NUM bjmsr-311 402 51 1 1 NUM bjmsr-311 402 52 1 1 NUM bjmsr-311 402 53 1 1 NUM bjmsr-311 402 54 2 2 NUM bjmsr-311 402 55 1 1 NUM bjmsr-311 402 56 1 1 NUM bjmsr-311 402 57 1 1 NUM bjmsr-311 402 58 1 1 NUM bjmsr-311 402 59 1 1 NUM bjmsr-311 402 60 2 2 NUM bjmsr-311 402 61 2 2 NUM bjmsr-311 402 62 1 1 NUM bjmsr-311 402 63 2 2 NUM bjmsr-311 402 64 2 2 NUM bjmsr-311 402 65 2 2 NUM bjmsr-311 402 66 1 1 NUM bjmsr-311 402 67 2 2 NUM bjmsr-311 402 68 3 3 NUM bjmsr-311 402 69 2 2 NUM bjmsr-311 402 70 1 1 NUM bjmsr-311 402 71 2 2 NUM bjmsr-311 402 72 2 2 NUM bjmsr-311 402 73 2 2 NUM bjmsr-311 402 74 11 11 NUM bjmsr-311 402 75 1 1 NUM bjmsr-311 402 76 1 1 NUM bjmsr-311 402 77 1 1 NUM bjmsr-311 402 78 2 2 NUM bjmsr-311 402 79 1 1 NUM bjmsr-311 402 80 1 1 NUM bjmsr-311 402 81 1 1 NUM bjmsr-311 402 82 1 1 NUM bjmsr-311 402 83 1 1 NUM bjmsr-311 402 84 1 1 NUM bjmsr-311 402 85 2 2 NUM bjmsr-311 402 86 1 1 NUM bjmsr-311 402 87 1 1 NUM bjmsr-311 402 88 1 1 NUM bjmsr-311 402 89 3 3 NUM bjmsr-311 402 90 1 1 NUM bjmsr-311 402 91 1 1 NUM bjmsr-311 402 92 1 1 NUM bjmsr-311 402 93 2 2 NUM bjmsr-311 403 1 k k NOUN bjmsr-311 403 2 k k PROPN bjmsr-311 404 1 k k PROPN bjmsr-311 405 1 i i PRON bjmsr-311 405 2 k k PROPN bjmsr-311 406 1 k k PROPN bjmsr-311 406 2 k k PROPN bjmsr-311 407 1 ki ki PROPN bjmsr-311 408 1 k k PROPN bjmsr-311 409 1 k k PROPN bjmsr-311 410 1 k k PROPN bjmsr-311 411 1 i i PRON bjmsr-311 411 2 k k PROPN bjmsr-311 412 1 k k PROPN bjmsr-311 413 1 k k PROPN bjmsr-311 414 1 k k PROPN bjmsr-311 414 2 k k PROPN bjmsr-311 415 1 k k PROPN bjmsr-311 415 2 ki ki PROPN bjmsr-311 416 1 k k PROPN bjmsr-311 416 2 k k PROPN bjmsr-311 417 1 k k PROPN bjmsr-311 418 1 i i PRON bjmsr-311 418 2 k k INTJ bjmsr-311 419 1 i i PRON bjmsr-311 419 2 k k PROPN bjmsr-311 420 1 k k PROPN bjmsr-311 421 1 k k PROPN bjmsr-311 422 1 k k PROPN bjmsr-311 422 2 k k PROPN bjmsr-311 423 1 k k PROPN bjmsr-311 423 2 ki ki PROPN bjmsr-311 424 1 k k PROPN bjmsr-311 424 2 k k PROPN bjmsr-311 425 1 k k PROPN bjmsr-311 426 1 i i PRON bjmsr-311 426 2 k k PROPN bjmsr-311 427 1 k k PROPN bjmsr-311 427 2 k k PROPN bjmsr-311 428 1 k k PROPN bjmsr-311 428 2 k k PROPN bjmsr-311 429 1 k k PROPN bjmsr-311 429 2 w w PUNCT bjmsr-311 429 3 x x PUNCT bjmsr-311 429 4 x x PUNCT bjmsr-311 429 5 x x SYM bjmsr-311 429 6 xx xx NUM bjmsr-311 429 7 x x NOUN bjmsr-311 429 8 x x PUNCT bjmsr-311 429 9 x x PUNCT bjmsr-311 429 10 x x PUNCT bjmsr-311 429 11 x x PUNCT bjmsr-311 429 12 x x PUNCT bjmsr-311 429 13 x x PUNCT bjmsr-311 429 14 x x PUNCT bjmsr-311 429 15 x x PUNCT bjmsr-311 429 16 x x SYM bjmsr-311 429 17 xx xx NUM bjmsr-311 429 18 x x NOUN bjmsr-311 429 19 x x PUNCT bjmsr-311 429 20 x x PUNCT bjmsr-311 429 21 x x PUNCT bjmsr-311 429 22 x x PUNCT bjmsr-311 429 23 x x PUNCT bjmsr-311 429 24 x x PUNCT bjmsr-311 429 25 x x PUNCT bjmsr-311 429 26 x x PUNCT bjmsr-311 429 27 x x PUNCT bjmsr-311 429 28 x x PUNCT bjmsr-311 429 29 x x SYM bjmsr-311 429 30 xx xx NUM bjmsr-311 429 31 x x NOUN bjmsr-311 429 32 x x PUNCT bjmsr-311 429 33 x x PUNCT bjmsr-311 429 34 x x PUNCT bjmsr-311 429 35 x x PUNCT bjmsr-311 429 36 x x PUNCT bjmsr-311 429 37 x x PUNCT bjmsr-311 429 38 x x PUNCT bjmsr-311 429 39 x x PUNCT bjmsr-311 429 40 x x PUNCT bjmsr-311 429 41 x x SYM bjmsr-311 429 42   PRON bjmsr-311 429 43   NOUN bjmsr-311 429 44   PUNCT bjmsr-311 429 45   NOUN bjmsr-311 429 46   PUNCT bjmsr-311 429 47   NOUN bjmsr-311 429 48   VERB bjmsr-311 429 49   PROPN bjmsr-311 429 50   PROPN bjmsr-311 429 51   PUNCT bjmsr-311 429 52   PROPN bjmsr-311 429 53   PROPN bjmsr-311 429 54   PROPN bjmsr-311 429 55   PROPN bjmsr-311 429 56   PROPN bjmsr-311 429 57   PROPN bjmsr-311 429 58   PROPN bjmsr-311 429 59   PROPN bjmsr-311 429 60   NUM bjmsr-311 429 61   NOUN bjmsr-311 429 62   NOUN bjmsr-311 429 63   VERB bjmsr-311 429 64   PROPN bjmsr-311 429 65   PROPN bjmsr-311 429 66   PROPN bjmsr-311 429 67   PROPN bjmsr-311 429 68   PROPN bjmsr-311 429 69 1 1 NUM bjmsr-311 429 70 1k 1k NUM bjmsr-311 429 71   NOUN bjmsr-311 429 72   PROPN bjmsr-311 430 1   PROPN bjmsr-311 430 2   PROPN bjmsr-311 431 1   PROPN bjmsr-311 432 1   INTJ bjmsr-311 433 1   PROPN bjmsr-311 434 1   INTJ bjmsr-311 435 1   PROPN bjmsr-311 435 2   PROPN bjmsr-311 436 1   PROPN bjmsr-311 436 2   NOUN bjmsr-311 436 3 ( ( PUNCT bjmsr-311 436 4 95 95 NUM bjmsr-311 436 5 ) ) PUNCT bjmsr-311 436 6 by by ADP bjmsr-311 436 7 inspection inspection NOUN bjmsr-311 436 8 of of ADP bjmsr-311 436 9 ( ( PUNCT bjmsr-311 436 10 93 93 NUM bjmsr-311 436 11 ) ) PUNCT bjmsr-311 436 12 , , PUNCT bjmsr-311 436 13 ( ( PUNCT bjmsr-311 436 14 94 94 NUM bjmsr-311 436 15 ) ) PUNCT bjmsr-311 436 16 and and CCONJ bjmsr-311 436 17 ( ( PUNCT bjmsr-311 436 18 95 95 NUM bjmsr-311 436 19 ) ) PUNCT bjmsr-311 436 20 it it PRON bjmsr-311 436 21 is be AUX bjmsr-311 436 22 obvious obvious ADJ bjmsr-311 436 23 that that SCONJ bjmsr-311 436 24 calculation calculation NOUN bjmsr-311 436 25 of of ADP bjmsr-311 436 26 r r NOUN bjmsr-311 436 27 i i PRON bjmsr-311 436 28 s1s2 s1s2 PROPN bjmsr-311 436 29 ... ... PUNCT bjmsr-311 436 30 sh sh PROPN bjmsr-311 436 31 and and CCONJ bjmsr-311 436 32 wi wi PROPN bjmsr-311 436 33 s1s2 s1s2 PROPN bjmsr-311 436 34 ... ... PUNCT bjmsr-311 436 35 sh sh INTJ bjmsr-311 436 36 where where SCONJ bjmsr-311 436 37 0 0 NUM bjmsr-311 436 38 < < X bjmsr-311 436 39 h≤m-1 h≤m-1 X bjmsr-311 436 40 which which PRON bjmsr-311 436 41 are be AUX bjmsr-311 436 42 necessary necessary ADJ bjmsr-311 436 43 for for SCONJ bjmsr-311 436 44 h h NOUN bjmsr-311 436 45 parameters parameter NOUN bjmsr-311 436 46 regression regression NOUN bjmsr-311 436 47 may may AUX bjmsr-311 436 48 be be AUX bjmsr-311 436 49 derived derive VERB bjmsr-311 436 50 from from ADP bjmsr-311 436 51 the the DET bjmsr-311 436 52 m m PROPN bjmsr-311 436 53 parameters parameter NOUN bjmsr-311 436 54 model model NOUN bjmsr-311 436 55 steps step NOUN bjmsr-311 436 56 of of ADP bjmsr-311 436 57 computation computation NOUN bjmsr-311 436 58 . . PUNCT bjmsr-311 437 1 property property NOUN bjmsr-311 437 2 3 3 NUM bjmsr-311 437 3 by by ADP bjmsr-311 437 4 any any DET bjmsr-311 437 5 commutation commutation NOUN bjmsr-311 437 6 for for ADP bjmsr-311 437 7 kj kj PROPN bjmsr-311 437 8 for for ADP bjmsr-311 437 9 j=1, j=1, NOUN bjmsr-311 437 10 ... ... PUNCT bjmsr-311 437 11 ,m-1 ,m-1 PUNCT bjmsr-311 437 12 , , PUNCT bjmsr-311 437 13 values value NOUN bjmsr-311 437 14 of of ADP bjmsr-311 437 15 ri ri PROPN bjmsr-311 437 16 s1s2 s1s2 PROPN bjmsr-311 437 17 ... ... PUNCT bjmsr-311 437 18 s(m-1 s(m-1 NOUN bjmsr-311 437 19 ) ) PUNCT bjmsr-311 437 20 defined define VERB bjmsr-311 437 21 by by ADP bjmsr-311 437 22 ( ( PUNCT bjmsr-311 437 23 92 92 NUM bjmsr-311 437 24 ) ) PUNCT bjmsr-311 437 25 for for ADP bjmsr-311 437 26 all all DET bjmsr-311 437 27 i≠k1,k2, i≠k1,k2, NOUN bjmsr-311 437 28 ... ... PUNCT bjmsr-311 437 29 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 437 30 ) ) PUNCT bjmsr-311 437 31 remain remain VERB bjmsr-311 437 32 unchanged unchanged ADJ bjmsr-311 437 33 . . PUNCT bjmsr-311 438 1 this this DET bjmsr-311 438 2 calculation calculation NOUN bjmsr-311 438 3 can can AUX bjmsr-311 438 4 be be AUX bjmsr-311 438 5 made make VERB bjmsr-311 438 6 by by ADP bjmsr-311 438 7 deleting delete VERB bjmsr-311 438 8 the the DET bjmsr-311 438 9 suitable suitable ADJ bjmsr-311 438 10 terms term NOUN bjmsr-311 438 11 in in ADP bjmsr-311 438 12 ( ( PUNCT bjmsr-311 438 13 93 93 NUM bjmsr-311 438 14 ) ) PUNCT bjmsr-311 438 15 and and CCONJ bjmsr-311 438 16 ( ( PUNCT bjmsr-311 438 17 94 94 NUM bjmsr-311 438 18 ) ) PUNCT bjmsr-311 438 19 after after ADP bjmsr-311 438 20 taking take VERB bjmsr-311 438 21 common common ADJ bjmsr-311 438 22 denominator denominator NOUN bjmsr-311 438 23 . . PUNCT bjmsr-311 439 1 because because SCONJ bjmsr-311 439 2 of of ADP bjmsr-311 439 3 this this DET bjmsr-311 439 4 property property NOUN bjmsr-311 439 5 , , PUNCT bjmsr-311 439 6 we we PRON bjmsr-311 439 7 can can AUX bjmsr-311 439 8 commute commute VERB bjmsr-311 439 9 for for ADP bjmsr-311 439 10 the the DET bjmsr-311 439 11 values value NOUN bjmsr-311 439 12 of of ADP bjmsr-311 439 13 k1, k1, NOUN bjmsr-311 439 14 ... ... PUNCT bjmsr-311 439 15 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 439 16 ) ) PUNCT bjmsr-311 439 17 in in ADP bjmsr-311 439 18 the the DET bjmsr-311 439 19 process process NOUN bjmsr-311 439 20 of of ADP bjmsr-311 439 21 computation computation NOUN bjmsr-311 439 22 without without ADP bjmsr-311 439 23 changing change VERB bjmsr-311 439 24 the the DET bjmsr-311 439 25 value value NOUN bjmsr-311 439 26 of of ADP bjmsr-311 439 27 ri ri NOUN bjmsr-311 439 28 s1 s1 PROPN bjmsr-311 439 29 ... ... PUNCT bjmsr-311 439 30 s(m-1 s(m-1 PROPN bjmsr-311 439 31 ) ) PUNCT bjmsr-311 439 32 . . PUNCT bjmsr-311 440 1 property property NOUN bjmsr-311 440 2 4 4 NUM bjmsr-311 440 3 by by ADP bjmsr-311 440 4 any any DET bjmsr-311 440 5 commutation commutation NOUN bjmsr-311 440 6 for for ADP bjmsr-311 440 7 kj kj PROPN bjmsr-311 440 8 for for ADP bjmsr-311 440 9 j=1, j=1, NOUN bjmsr-311 440 10 ... ... PUNCT bjmsr-311 440 11 ,m-1 ,m-1 PUNCT bjmsr-311 440 12 , , PUNCT bjmsr-311 440 13 values value NOUN bjmsr-311 440 14 of of ADP bjmsr-311 440 15 wi wi PROPN bjmsr-311 440 16 k1 k1 PROPN bjmsr-311 440 17 ... ... PUNCT bjmsr-311 440 18 k(m-1 k(m-1 PROPN bjmsr-311 440 19 ) ) PUNCT bjmsr-311 440 20 for for ADP bjmsr-311 440 21 all all DET bjmsr-311 440 22 i=1, i=1, NOUN bjmsr-311 440 23 ... ... PUNCT bjmsr-311 440 24 ,n ,n PUNCT bjmsr-311 440 25 defined define VERB bjmsr-311 440 26 by by ADP bjmsr-311 440 27 ( ( PUNCT bjmsr-311 440 28 91 91 NUM bjmsr-311 440 29 ) ) PUNCT bjmsr-311 440 30 remain remain VERB bjmsr-311 440 31 unchanged unchanged ADJ bjmsr-311 440 32 . . PUNCT bjmsr-311 441 1 this this DET bjmsr-311 441 2 conclusion conclusion NOUN bjmsr-311 441 3 is be AUX bjmsr-311 441 4 made make VERB bjmsr-311 441 5 by by ADP bjmsr-311 441 6 multiplication multiplication NOUN bjmsr-311 441 7 of of ADP bjmsr-311 441 8 sequential sequential ADJ bjmsr-311 441 9 parentheses parenthesis NOUN bjmsr-311 441 10 of of ADP bjmsr-311 441 11 ( ( PUNCT bjmsr-311 441 12 97 97 NUM bjmsr-311 441 13 ) ) PUNCT bjmsr-311 441 14 and and CCONJ bjmsr-311 441 15 deleting delete VERB bjmsr-311 441 16 the the DET bjmsr-311 441 17 suitable suitable ADJ bjmsr-311 441 18 terms term NOUN bjmsr-311 441 19 . . PUNCT bjmsr-311 442 1 this this DET bjmsr-311 442 2 property property NOUN bjmsr-311 442 3 accompanying accompany VERB bjmsr-311 442 4 with with ADP bjmsr-311 442 5 property property NOUN bjmsr-311 442 6 3 3 NUM bjmsr-311 442 7 guarantees guarantee VERB bjmsr-311 442 8 that that SCONJ bjmsr-311 442 9 any any DET bjmsr-311 442 10 commutation commutation NOUN bjmsr-311 442 11 for for ADP bjmsr-311 442 12 k1, k1, NOUN bjmsr-311 442 13 ... ... PUNCT bjmsr-311 442 14 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 442 15 ) ) PUNCT bjmsr-311 442 16 does do AUX bjmsr-311 442 17 not not PART bjmsr-311 442 18 change change VERB bjmsr-311 442 19 the the DET bjmsr-311 442 20 necessary necessary ADJ bjmsr-311 442 21 items item NOUN bjmsr-311 442 22 of of ADP bjmsr-311 442 23 ( ( PUNCT bjmsr-311 442 24 91 91 NUM bjmsr-311 442 25 ) ) PUNCT bjmsr-311 442 26 and and CCONJ bjmsr-311 442 27 ( ( PUNCT bjmsr-311 442 28 92 92 NUM bjmsr-311 442 29 ) ) PUNCT bjmsr-311 442 30 in in ADP bjmsr-311 442 31 the the DET bjmsr-311 442 32 computation computation NOUN bjmsr-311 442 33 of of ADP bjmsr-311 442 34 weighted weight VERB bjmsr-311 442 35 median median ADJ bjmsr-311 442 36 problem problem NOUN bjmsr-311 442 37 ( ( PUNCT bjmsr-311 442 38 90 90 NUM bjmsr-311 442 39 ) ) PUNCT bjmsr-311 442 40 . . PUNCT bjmsr-311 443 1 property property NOUN bjmsr-311 443 2 5 5 NUM bjmsr-311 443 3 value value NOUN bjmsr-311 443 4 of of ADP bjmsr-311 443 5 rk(m-1 rk(m-1 PROPN bjmsr-311 443 6 ) ) PUNCT bjmsr-311 443 7 s1 s1 PROPN bjmsr-311 443 8 ... ... PUNCT bjmsr-311 443 9 s(m-1 s(m-1 PROPN bjmsr-311 443 10 ) ) PUNCT bjmsr-311 443 11 is be AUX bjmsr-311 443 12 equal equal ADJ bjmsr-311 443 13 to to ADP bjmsr-311 443 14 zero zero NUM bjmsr-311 443 15 . . PUNCT bjmsr-311 444 1 by by ADP bjmsr-311 444 2 substituting substitute VERB bjmsr-311 444 3 i i PROPN bjmsr-311 444 4 = = PROPN bjmsr-311 444 5 k(m-1 k(m-1 X bjmsr-311 444 6 ) ) PUNCT bjmsr-311 444 7 in in ADP bjmsr-311 444 8 ( ( PUNCT bjmsr-311 444 9 93 93 NUM bjmsr-311 444 10 ) ) PUNCT bjmsr-311 444 11 or or CCONJ bjmsr-311 444 12 ( ( PUNCT bjmsr-311 444 13 94 94 NUM bjmsr-311 444 14 ) ) PUNCT bjmsr-311 444 15 this this DET bjmsr-311 444 16 property property NOUN bjmsr-311 444 17 is be AUX bjmsr-311 444 18 concluded conclude VERB bjmsr-311 444 19 . . PUNCT bjmsr-311 445 1 since since SCONJ bjmsr-311 445 2 , , PUNCT bjmsr-311 445 3 this this DET bjmsr-311 445 4 term term NOUN bjmsr-311 445 5 is be AUX bjmsr-311 445 6 equal equal ADJ bjmsr-311 445 7 to to ADP bjmsr-311 445 8 zero zero NUM bjmsr-311 445 9 we we PRON bjmsr-311 445 10 should should AUX bjmsr-311 445 11 be be AUX bjmsr-311 445 12 aware aware ADJ bjmsr-311 445 13 of of ADP bjmsr-311 445 14 divide divide ADJ bjmsr-311 445 15 check check NOUN bjmsr-311 445 16 ( ( PUNCT bjmsr-311 445 17 dividing divide VERB bjmsr-311 445 18 by by ADP bjmsr-311 445 19 zero zero NUM bjmsr-311 445 20 ) ) PUNCT bjmsr-311 445 21 in in ADP bjmsr-311 445 22 the the DET bjmsr-311 445 23 process process NOUN bjmsr-311 445 24 of of ADP bjmsr-311 445 25 computation computation NOUN bjmsr-311 445 26 of of ADP bjmsr-311 445 27 rk1 rk1 PROPN bjmsr-311 445 28 s1,rk2 s1,rk2 PROPN bjmsr-311 445 29 s1s2, s1s2, VERB bjmsr-311 445 30 ... ... PUNCT bjmsr-311 445 31 ,rk(m1 ,rk(m1 PUNCT bjmsr-311 445 32 ) ) PUNCT bjmsr-311 445 33 s1s2 s1s2 PROPN bjmsr-311 445 34 ... ... PUNCT bjmsr-311 445 35 s(m-1 s(m-1 PROPN bjmsr-311 445 36 ) ) PUNCT bjmsr-311 445 37 . . PUNCT bjmsr-311 446 1 property property NOUN bjmsr-311 446 2 6 6 NUM bjmsr-311 446 3 values value NOUN bjmsr-311 446 4 of of ADP bjmsr-311 446 5 wh wh PROPN bjmsr-311 446 6 k1k2 k1k2 PROPN bjmsr-311 446 7 ... ... PUNCT bjmsr-311 446 8 k(m-1)=0 k(m-1)=0 ADJ bjmsr-311 446 9 for for ADP bjmsr-311 446 10 all all DET bjmsr-311 446 11 h h NOUN bjmsr-311 446 12 = = NOUN bjmsr-311 446 13 k1,k2, k1,k2, NOUN bjmsr-311 446 14 ... ... PUNCT bjmsr-311 446 15 ,k(m-1 ,k(m-1 PROPN bjmsr-311 446 16 ) ) PUNCT bjmsr-311 446 17 . . PUNCT bjmsr-311 447 1 if if SCONJ bjmsr-311 447 2 h h NOUN bjmsr-311 447 3 is be AUX bjmsr-311 447 4 equal equal ADJ bjmsr-311 447 5 to to ADP bjmsr-311 447 6 one one NUM bjmsr-311 447 7 of of ADP bjmsr-311 447 8 the the DET bjmsr-311 447 9 k1,k2, k1,k2, NOUN bjmsr-311 447 10 ... ... PUNCT bjmsr-311 447 11 ,k(m-1 ,k(m-1 PROPN bjmsr-311 447 12 ) ) PUNCT bjmsr-311 447 13 , , PUNCT bjmsr-311 447 14 then then ADV bjmsr-311 447 15 one one NUM bjmsr-311 447 16 of of ADP bjmsr-311 447 17 the the DET bjmsr-311 447 18 parentheses parenthesis NOUN bjmsr-311 447 19 of of ADP bjmsr-311 447 20 ( ( PUNCT bjmsr-311 447 21 95 95 NUM bjmsr-311 447 22 ) ) PUNCT bjmsr-311 447 23 is be AUX bjmsr-311 447 24 equal equal ADJ bjmsr-311 447 25 to to ADP bjmsr-311 447 26 zero zero NUM bjmsr-311 447 27 , , PUNCT bjmsr-311 447 28 and and CCONJ bjmsr-311 447 29 this this DET bjmsr-311 447 30 property property NOUN bjmsr-311 447 31 is be AUX bjmsr-311 447 32 assured assure VERB bjmsr-311 447 33 . . PUNCT bjmsr-311 448 1 according accord VERB bjmsr-311 448 2 to to ADP bjmsr-311 448 3 this this DET bjmsr-311 448 4 property property NOUN bjmsr-311 448 5 to to PART bjmsr-311 448 6 avoid avoid VERB bjmsr-311 448 7 divide divide ADJ bjmsr-311 448 8 check check NOUN bjmsr-311 448 9 , , PUNCT bjmsr-311 448 10 without without ADP bjmsr-311 448 11 computing compute VERB bjmsr-311 448 12 wh wh PROPN bjmsr-311 448 13 k1k2 k1k2 PROPN bjmsr-311 448 14 ... ... PUNCT bjmsr-311 448 15 k(m-1 k(m-1 PROPN bjmsr-311 448 16 ) ) PUNCT bjmsr-311 448 17 for for ADP bjmsr-311 448 18 h h NOUN bjmsr-311 448 19 = = NOUN bjmsr-311 448 20 k1,k2, k1,k2, NOUN bjmsr-311 448 21 ... ... PUNCT bjmsr-311 448 22 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 448 23 ) ) PUNCT bjmsr-311 448 24 we we PRON bjmsr-311 448 25 can can AUX bjmsr-311 448 26 set set VERB bjmsr-311 448 27 these these DET bjmsr-311 448 28 terms term NOUN bjmsr-311 448 29 equal equal ADJ bjmsr-311 448 30 to to ADP bjmsr-311 448 31 zero zero NUM bjmsr-311 448 32 . . PUNCT bjmsr-311 449 1 property property NOUN bjmsr-311 449 2 7 7 NUM bjmsr-311 449 3 by by ADP bjmsr-311 449 4 any any DET bjmsr-311 449 5 commutation commutation NOUN bjmsr-311 449 6 for for ADP bjmsr-311 449 7 kj kj PROPN bjmsr-311 449 8 for for ADP bjmsr-311 449 9 j=1, j=1, NOUN bjmsr-311 449 10 ... ... PUNCT bjmsr-311 449 11 ,(m-1 ,(m-1 NUM bjmsr-311 449 12 ) ) PUNCT bjmsr-311 449 13 , , PUNCT bjmsr-311 449 14 the the DET bjmsr-311 449 15 mth mth NOUN bjmsr-311 449 16 point point NOUN bjmsr-311 449 17 derived derive VERB bjmsr-311 449 18 by by ADP bjmsr-311 449 19 minimizing minimize VERB bjmsr-311 449 20 ( ( PUNCT bjmsr-311 449 21 89 89 NUM bjmsr-311 449 22 ) ) PUNCT bjmsr-311 449 23 remains remain VERB bjmsr-311 449 24 unchanged unchanged ADJ bjmsr-311 449 25 . . PUNCT bjmsr-311 450 1 because because SCONJ bjmsr-311 450 2 , , PUNCT bjmsr-311 450 3 by by ADP bjmsr-311 450 4 this this DET bjmsr-311 450 5 commutation commutation NOUN bjmsr-311 450 6 values value NOUN bjmsr-311 450 7 of of ADP bjmsr-311 450 8 ri ri PROPN bjmsr-311 450 9 s1s2 s1s2 PROPN bjmsr-311 450 10 ... ... PUNCT bjmsr-311 450 11 s(m-1 s(m-1 PROPN bjmsr-311 450 12 ) ) PUNCT bjmsr-311 450 13 and and CCONJ bjmsr-311 450 14 wi wi PROPN bjmsr-311 450 15 k1k2 k1k2 PROPN bjmsr-311 450 16 ... ... PUNCT bjmsr-311 450 17 k(m-1 k(m-1 PROPN bjmsr-311 450 18 ) ) PUNCT bjmsr-311 450 19 remain remain VERB bjmsr-311 450 20 unchanged unchanged ADJ bjmsr-311 450 21 ( ( PUNCT bjmsr-311 450 22 properties property NOUN bjmsr-311 450 23 3,4,5 3,4,5 NUM bjmsr-311 450 24 and and CCONJ bjmsr-311 450 25 6 6 NUM bjmsr-311 450 26 ) ) PUNCT bjmsr-311 450 27 . . PUNCT bjmsr-311 451 1 property property NOUN bjmsr-311 451 2 8 8 NUM bjmsr-311 451 3 updating update VERB bjmsr-311 451 4 procedure procedure NOUN bjmsr-311 451 5 to to PART bjmsr-311 451 6 evaluate evaluate VERB bjmsr-311 451 7 different different ADJ bjmsr-311 451 8 subsets subset NOUN bjmsr-311 451 9 of of ADP bjmsr-311 451 10 sample sample NOUN bjmsr-311 451 11 observations observation NOUN bjmsr-311 451 12 can can AUX bjmsr-311 451 13 be be AUX bjmsr-311 451 14 simply simply ADV bjmsr-311 451 15 done do VERB bjmsr-311 451 16 by by ADP bjmsr-311 451 17 assigning assign VERB bjmsr-311 451 18 zero zero NUM bjmsr-311 451 19 values value NOUN bjmsr-311 451 20 to to ADP bjmsr-311 451 21 their their PRON bjmsr-311 451 22 wh wh NOUN bjmsr-311 451 23 k1k2 k1k2 PROPN bjmsr-311 451 24 ... ... PUNCT bjmsr-311 451 25 k(m-1 k(m-1 PROPN bjmsr-311 451 26 ) ) PUNCT bjmsr-311 451 27 in in ADP bjmsr-311 451 28 ( ( PUNCT bjmsr-311 451 29 90 90 NUM bjmsr-311 451 30 ) ) PUNCT bjmsr-311 451 31 for for ADP bjmsr-311 451 32 deleting delete VERB bjmsr-311 451 33 points point NOUN bjmsr-311 451 34 . . PUNCT bjmsr-311 452 1 this this PRON bjmsr-311 452 2 makes make VERB bjmsr-311 452 3 those those DET bjmsr-311 452 4 unwanted unwanted ADJ bjmsr-311 452 5 points point NOUN bjmsr-311 452 6 h h NOUN bjmsr-311 452 7 's be AUX bjmsr-311 452 8 be be AUX bjmsr-311 452 9 unaffected unaffected ADJ bjmsr-311 452 10 in in ADP bjmsr-311 452 11 the the DET bjmsr-311 452 12 calculation calculation NOUN bjmsr-311 452 13 . . PUNCT bjmsr-311 453 1 property property NOUN bjmsr-311 453 2 9 9 NUM bjmsr-311 453 3 according accord VERB bjmsr-311 453 4 to to ADP bjmsr-311 453 5 properties property NOUN bjmsr-311 453 6 6 6 NUM bjmsr-311 453 7 and and CCONJ bjmsr-311 453 8 8 8 NUM bjmsr-311 453 9 , , PUNCT bjmsr-311 453 10 since since SCONJ bjmsr-311 453 11 the the DET bjmsr-311 453 12 value value NOUN bjmsr-311 453 13 of of ADP bjmsr-311 453 14 wh wh PROPN bjmsr-311 453 15 k1k2 k1k2 PROPN bjmsr-311 453 16 ... ... PUNCT bjmsr-311 453 17 k(m-1)=0 k(m-1)=0 ADJ bjmsr-311 453 18 for for ADP bjmsr-311 453 19 all all DET bjmsr-311 453 20 h h NOUN bjmsr-311 453 21 = = NOUN bjmsr-311 453 22 k1,k2, k1,k2, NOUN bjmsr-311 453 23 ... ... PUNCT bjmsr-311 453 24 ,k(m-1 ,k(m-1 PROPN bjmsr-311 453 25 ) ) PUNCT bjmsr-311 453 26 ; ; PUNCT bjmsr-311 453 27 the the DET bjmsr-311 453 28 point point NOUN bjmsr-311 453 29 m m VERB bjmsr-311 453 30 which which PRON bjmsr-311 453 31 derives derive VERB bjmsr-311 453 32 from from ADP bjmsr-311 453 33 solving solve VERB bjmsr-311 453 34 weighted weight VERB bjmsr-311 453 35 median median ADJ bjmsr-311 453 36 problem problem NOUN bjmsr-311 453 37 ( ( PUNCT bjmsr-311 453 38 90 90 NUM bjmsr-311 453 39 ) ) PUNCT bjmsr-311 453 40 will will AUX bjmsr-311 453 41 not not PART bjmsr-311 453 42 be be AUX bjmsr-311 453 43 equal equal ADJ bjmsr-311 453 44 to to ADP bjmsr-311 453 45 k1,k2, k1,k2, NOUN bjmsr-311 453 46 ... ... PUNCT bjmsr-311 453 47 ,k(m-1 ,k(m-1 PROPN bjmsr-311 453 48 ) ) PUNCT bjmsr-311 453 49 . . PUNCT bjmsr-311 454 1 this this DET bjmsr-311 454 2 property property NOUN bjmsr-311 454 3 guarantees guarantee VERB bjmsr-311 454 4 that that SCONJ bjmsr-311 454 5 when when SCONJ bjmsr-311 454 6 we we PRON bjmsr-311 454 7 enter enter VERB bjmsr-311 454 8 an an DET bjmsr-311 454 9 observation observation NOUN bjmsr-311 454 10 into into ADP bjmsr-311 454 11 the the DET bjmsr-311 454 12 basis basis NOUN bjmsr-311 454 13 , , PUNCT bjmsr-311 454 14 we we PRON bjmsr-311 454 15 do do AUX bjmsr-311 454 16 not not PART bjmsr-311 454 17 find find VERB bjmsr-311 454 18 this this DET bjmsr-311 454 19 point point NOUN bjmsr-311 454 20 again again ADV bjmsr-311 454 21 in in ADP bjmsr-311 454 22 the the DET bjmsr-311 454 23 same same ADJ bjmsr-311 454 24 iteration iteration NOUN bjmsr-311 454 25 . . PUNCT bjmsr-311 455 1 property property NOUN bjmsr-311 455 2 10 10 NUM bjmsr-311 455 3 if if SCONJ bjmsr-311 455 4 all all DET bjmsr-311 455 5 kj kj NOUN bjmsr-311 455 6 for for ADP bjmsr-311 455 7 j=1, j=1, NOUN bjmsr-311 455 8 ... ... PUNCT bjmsr-311 455 9 ,m-1 ,m-1 PUNCT bjmsr-311 455 10 are be AUX bjmsr-311 455 11 equal equal ADJ bjmsr-311 455 12 in in ADP bjmsr-311 455 13 starting start VERB bjmsr-311 455 14 time time NOUN bjmsr-311 455 15 , , PUNCT bjmsr-311 455 16 no no DET bjmsr-311 455 17 problem problem NOUN bjmsr-311 455 18 occurs occur VERB bjmsr-311 455 19 in in ADP bjmsr-311 455 20 the the DET bjmsr-311 455 21 process process NOUN bjmsr-311 455 22 of of ADP bjmsr-311 455 23 computation computation NOUN bjmsr-311 455 24 , , PUNCT bjmsr-311 455 25 but but CCONJ bjmsr-311 455 26 the the DET bjmsr-311 455 27 execution execution NOUN bjmsr-311 455 28 time time NOUN bjmsr-311 455 29 may may AUX bjmsr-311 455 30 be be AUX bjmsr-311 455 31 increased increase VERB bjmsr-311 455 32 . . PUNCT bjmsr-311 456 1 conversely conversely ADV bjmsr-311 456 2 , , PUNCT bjmsr-311 456 3 if if SCONJ bjmsr-311 456 4 the the DET bjmsr-311 456 5 kj kj PROPN bjmsr-311 456 6 points point NOUN bjmsr-311 456 7 are be AUX bjmsr-311 456 8 selected select VERB bjmsr-311 456 9 in in ADP bjmsr-311 456 10 such such DET bjmsr-311 456 11 a a DET bjmsr-311 456 12 way way NOUN bjmsr-311 456 13 that that PRON bjmsr-311 456 14 they they PRON bjmsr-311 456 15 are be AUX bjmsr-311 456 16 near near ADP bjmsr-311 456 17 the the DET bjmsr-311 456 18 minimum minimum NOUN bjmsr-311 456 19 of of ADP bjmsr-311 456 20 s s PROPN bjmsr-311 456 21 , , PUNCT bjmsr-311 456 22 the the DET bjmsr-311 456 23 algorithm algorithm NOUN bjmsr-311 456 24 converges converge VERB bjmsr-311 456 25 to to ADP bjmsr-311 456 26 the the DET bjmsr-311 456 27 optimal optimal ADJ bjmsr-311 456 28 solution solution NOUN bjmsr-311 456 29 with with ADP bjmsr-311 456 30 fewer few ADJ bjmsr-311 456 31 iterations iteration NOUN bjmsr-311 456 32 . . PUNCT bjmsr-311 457 1 property property NOUN bjmsr-311 457 2 11 11 NUM bjmsr-311 457 3 values value NOUN bjmsr-311 457 4 of of ADP bjmsr-311 457 5 wi wi PROPN bjmsr-311 457 6 k1k2 k1k2 PROPN bjmsr-311 457 7 ... ... PUNCT bjmsr-311 457 8 k(m-1 k(m-1 PROPN bjmsr-311 457 9 ) ) PUNCT bjmsr-311 457 10 and and CCONJ bjmsr-311 457 11 ri ri PROPN bjmsr-311 457 12 s1s2 s1s2 PROPN bjmsr-311 457 13 ... ... PUNCT bjmsr-311 457 14 s(m-1 s(m-1 PROPN bjmsr-311 457 15 ) ) PUNCT bjmsr-311 457 16 , , PUNCT bjmsr-311 457 17 which which PRON bjmsr-311 457 18 are be AUX bjmsr-311 457 19 essential essential ADJ bjmsr-311 457 20 to to ADP bjmsr-311 457 21 solving solve VERB bjmsr-311 457 22 the the DET bjmsr-311 457 23 weighted weight VERB bjmsr-311 457 24 median median ADJ bjmsr-311 457 25 problem problem NOUN bjmsr-311 457 26 of of ADP bjmsr-311 457 27 ( ( PUNCT bjmsr-311 457 28 90 90 NUM bjmsr-311 457 29 ) ) PUNCT bjmsr-311 457 30 can can AUX bjmsr-311 457 31 be be AUX bjmsr-311 457 32 retrieved retrieve VERB bjmsr-311 457 33 from from ADP bjmsr-311 457 34 their their PRON bjmsr-311 457 35 values value NOUN bjmsr-311 457 36 in in ADP bjmsr-311 457 37 the the DET bjmsr-311 457 38 previous previous ADJ bjmsr-311 457 39 iteration iteration NOUN bjmsr-311 457 40 . . PUNCT bjmsr-311 458 1 that that PRON bjmsr-311 458 2 is be AUX bjmsr-311 458 3 when when SCONJ bjmsr-311 458 4 the the DET bjmsr-311 458 5 point point NOUN bjmsr-311 458 6 kh kh PROPN bjmsr-311 458 7 is be AUX bjmsr-311 458 8 discarded discard VERB bjmsr-311 458 9 from from ADP bjmsr-311 458 10 the the DET bjmsr-311 458 11 basis basis NOUN bjmsr-311 458 12 and and CCONJ bjmsr-311 458 13 replaced replace VERB bjmsr-311 458 14 by by ADP bjmsr-311 458 15 kj kj PROPN bjmsr-311 458 16 , , PUNCT bjmsr-311 458 17 values value NOUN bjmsr-311 458 18 of of ADP bjmsr-311 458 19 copyright copyright NOUN bjmsr-311 458 20 © © PROPN bjmsr-311 458 21 cc cc PROPN bjmsr-311 458 22 - - PUNCT bjmsr-311 458 23 by by ADP bjmsr-311 458 24 - - PUNCT bjmsr-311 458 25 nc nc PROPN bjmsr-311 458 26 2019 2019 NUM bjmsr-311 458 27 , , PUNCT bjmsr-311 458 28 bjmsr bjmsr PROPN bjmsr-311 458 29 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 458 30 bangladesh bangladesh PROPN bjmsr-311 458 31 journal journal PROPN bjmsr-311 458 32 of of ADP bjmsr-311 458 33 multidisciplinary multidisciplinary ADJ bjmsr-311 458 34 scientific scientific ADJ bjmsr-311 458 35 research research NOUN bjmsr-311 458 36 vol vol NOUN bjmsr-311 458 37 . . PROPN bjmsr-311 459 1 1 1 NUM bjmsr-311 459 2 , , PUNCT bjmsr-311 459 3 no no INTJ bjmsr-311 459 4 . . NOUN bjmsr-311 459 5 1 1 NUM bjmsr-311 459 6 ; ; PUNCT bjmsr-311 459 7 2019 2019 NUM bjmsr-311 459 8 15 15 NUM bjmsr-311 459 9 wi wi PROPN bjmsr-311 459 10 k1k2 k1k2 PROPN bjmsr-311 459 11 ... ... PUNCT bjmsr-311 459 12 k(h-1 k(h-1 PROPN bjmsr-311 459 13 ) ) PUNCT bjmsr-311 459 14 and and CCONJ bjmsr-311 459 15 ri ri PROPN bjmsr-311 459 16 s1s2 s1s2 NOUN bjmsr-311 459 17 ... ... NOUN bjmsr-311 459 18 s(h-1 s(h-1 ADJ bjmsr-311 459 19 ) ) PUNCT bjmsr-311 459 20 do do AUX bjmsr-311 459 21 not not PART bjmsr-311 459 22 change change VERB bjmsr-311 459 23 and and CCONJ bjmsr-311 459 24 need need AUX bjmsr-311 459 25 not not PART bjmsr-311 459 26 be be AUX bjmsr-311 459 27 computed compute VERB bjmsr-311 459 28 again again ADV bjmsr-311 459 29 . . PUNCT bjmsr-311 460 1 applying apply VERB bjmsr-311 460 2 this this DET bjmsr-311 460 3 property property NOUN bjmsr-311 460 4 to to ADP bjmsr-311 460 5 algorithm algorithm NOUN bjmsr-311 460 6 4 4 NUM bjmsr-311 460 7 makes make VERB bjmsr-311 460 8 it it PRON bjmsr-311 460 9 more more ADV bjmsr-311 460 10 efficient efficient ADJ bjmsr-311 460 11 . . PUNCT bjmsr-311 461 1 property property NOUN bjmsr-311 461 2 12 12 NUM bjmsr-311 461 3 since since SCONJ bjmsr-311 461 4 at at ADP bjmsr-311 461 5 each each DET bjmsr-311 461 6 iteration iteration NOUN bjmsr-311 461 7 , , PUNCT bjmsr-311 461 8 values value NOUN bjmsr-311 461 9 of of ADP bjmsr-311 461 10 ri ri PROPN bjmsr-311 461 11 s1s2 s1s2 PROPN bjmsr-311 461 12 ... ... PUNCT bjmsr-311 461 13 s(m-1 s(m-1 PROPN bjmsr-311 461 14 ) ) PUNCT bjmsr-311 461 15 and and CCONJ bjmsr-311 461 16 wi wi PROPN bjmsr-311 461 17 k1k2 k1k2 PROPN bjmsr-311 461 18 ... ... PUNCT bjmsr-311 461 19 k(m-1 k(m-1 PROPN bjmsr-311 461 20 ) ) PUNCT bjmsr-311 461 21 should should AUX bjmsr-311 461 22 be be AUX bjmsr-311 461 23 computed compute VERB bjmsr-311 461 24 from from ADP bjmsr-311 461 25 the the DET bjmsr-311 461 26 source source NOUN bjmsr-311 461 27 input input NOUN bjmsr-311 461 28 data datum NOUN bjmsr-311 461 29 y y PROPN bjmsr-311 461 30 and and CCONJ bjmsr-311 461 31 x x PROPN bjmsr-311 461 32 , , PUNCT bjmsr-311 461 33 rounding round VERB bjmsr-311 461 34 error error NOUN bjmsr-311 461 35 does do AUX bjmsr-311 461 36 not not PART bjmsr-311 461 37 accumulate accumulate VERB bjmsr-311 461 38 , , PUNCT bjmsr-311 461 39 and and CCONJ bjmsr-311 461 40 convergence convergence NOUN bjmsr-311 461 41 does do AUX bjmsr-311 461 42 not not PART bjmsr-311 461 43 perturb perturb VERB bjmsr-311 461 44 . . PUNCT bjmsr-311 462 1 this this DET bjmsr-311 462 2 property property NOUN bjmsr-311 462 3 makes make VERB bjmsr-311 462 4 the the DET bjmsr-311 462 5 algorithm algorithm NOUN bjmsr-311 462 6 safe safe ADJ bjmsr-311 462 7 from from ADP bjmsr-311 462 8 the the DET bjmsr-311 462 9 accumulation accumulation NOUN bjmsr-311 462 10 of of ADP bjmsr-311 462 11 rounding round VERB bjmsr-311 462 12 error error NOUN bjmsr-311 462 13 , , PUNCT bjmsr-311 462 14 which which PRON bjmsr-311 462 15 exists exist VERB bjmsr-311 462 16 in in ADP bjmsr-311 462 17 simplex simplex NOUN bjmsr-311 462 18 - - PUNCT bjmsr-311 462 19 type type NOUN bjmsr-311 462 20 algorithms algorithm NOUN bjmsr-311 462 21 . . PUNCT bjmsr-311 463 1 property property NOUN bjmsr-311 463 2 13 13 NUM bjmsr-311 463 3 when when SCONJ bjmsr-311 463 4 m m VERB bjmsr-311 463 5 optimal optimal ADJ bjmsr-311 463 6 points point NOUN bjmsr-311 463 7 are be AUX bjmsr-311 463 8 reached reach VERB bjmsr-311 463 9 , , PUNCT bjmsr-311 463 10 the the DET bjmsr-311 463 11 optimal optimal ADJ bjmsr-311 463 12 values value NOUN bjmsr-311 463 13 of of ADP bjmsr-311 463 14 ß ß DET bjmsr-311 463 15 j^ j^ NOUN bjmsr-311 463 16 for for ADP bjmsr-311 463 17 j=1, j=1, NOUN bjmsr-311 463 18 ... ... PUNCT bjmsr-311 463 19 ,m ,m PUNCT bjmsr-311 463 20 can can AUX bjmsr-311 463 21 be be AUX bjmsr-311 463 22 computed compute VERB bjmsr-311 463 23 as as ADP bjmsr-311 463 24 a a DET bjmsr-311 463 25 recursive recursive ADJ bjmsr-311 463 26 system system NOUN bjmsr-311 463 27 of of ADP bjmsr-311 463 28 equations equation NOUN bjmsr-311 463 29 efficiently efficiently ADV bjmsr-311 463 30 . . PUNCT bjmsr-311 464 1 values value NOUN bjmsr-311 464 2 of of ADP bjmsr-311 464 3 ßj^ ßj^ NOUN bjmsr-311 464 4 will will AUX bjmsr-311 464 5 be be AUX bjmsr-311 464 6 , , PUNCT bjmsr-311 464 7 ( ( PUNCT bjmsr-311 464 8 1 1 X bjmsr-311 464 9 ) ) SYM bjmsr-311 464 10 1 1 NUM bjmsr-311 464 11 ( ( PUNCT bjmsr-311 464 12 2 2 NUM bjmsr-311 464 13 ) ) PUNCT bjmsr-311 464 14 ( ( PUNCT bjmsr-311 464 15 2 2 NUM bjmsr-311 464 16 ) ) PUNCT bjmsr-311 464 17 ( ( PUNCT bjmsr-311 464 18 1 1 X bjmsr-311 464 19 ) ) PUNCT bjmsr-311 464 20 ( ( PUNCT bjmsr-311 464 21 1)2 1)2 NUM bjmsr-311 464 22 ( ( PUNCT bjmsr-311 464 23 1 1 NUM bjmsr-311 464 24 ) ) PUNCT bjmsr-311 464 25 2 2 NUM bjmsr-311 464 26 22 22 NUM bjmsr-311 464 27 ( ( PUNCT bjmsr-311 464 28 1 1 NUM bjmsr-311 464 29 ) ) PUNCT bjmsr-311 464 30 3 3 NUM bjmsr-311 464 31 ( ( PUNCT bjmsr-311 464 32 2 2 NUM bjmsr-311 464 33 ) ) PUNCT bjmsr-311 464 34 32 32 NUM bjmsr-311 464 35 3 3 NUM bjmsr-311 464 36 1 1 NUM bjmsr-311 464 37 1 1 NUM bjmsr-311 464 38 11 11 NUM bjmsr-311 464 39 ( ( PUNCT bjmsr-311 464 40 1 1 NUM bjmsr-311 464 41 ) ) SYM bjmsr-311 464 42 2 2 NUM bjmsr-311 464 43 ( ( PUNCT bjmsr-311 464 44 2 2 NUM bjmsr-311 464 45 ) ) SYM bjmsr-311 464 46 2 2 NUM bjmsr-311 464 47 2 2 NUM bjmsr-311 464 48 21 21 NUM bjmsr-311 464 49 2 2 NUM bjmsr-311 464 50 ( ( PUNCT bjmsr-311 464 51 1 1 NUM bjmsr-311 464 52 ) ) PUNCT bjmsr-311 464 53 1 1 NUM bjmsr-311 464 54 ( ( PUNCT bjmsr-311 464 55 2)0 2)0 NUM bjmsr-311 464 56 1 1 NUM bjmsr-311 464 57 0 0 NUM bjmsr-311 464 58 0 0 NUM bjmsr-311 464 59 0 0 NUM bjmsr-311 464 60 0 0 NUM bjmsr-311 464 61 0 0 NUM bjmsr-311 464 62 0 0 NUM bjmsr-311 464 63 0 0 NUM bjmsr-311 464 64 0 0 NUM bjmsr-311 464 65 0 0 NUM bjmsr-311 464 66 0 0 NUM bjmsr-311 464 67 0 0 NUM bjmsr-311 464 68 0 0 NUM bjmsr-311 464 69 0 0 NUM bjmsr-311 464 70 0 0 NUM bjmsr-311 464 71 s s X bjmsr-311 464 72 m m VERB bjmsr-311 464 73 m m VERB bjmsr-311 464 74 m m VERB bjmsr-311 464 75 s s NOUN bjmsr-311 464 76 ms ms PROPN bjmsr-311 464 77 m m PROPN bjmsr-311 464 78 m m VERB bjmsr-311 464 79 k k NOUN bjmsr-311 465 1 mm mm INTJ bjmsr-311 466 1 k k PROPN bjmsr-311 466 2 m m PROPN bjmsr-311 466 3 s s VERB bjmsr-311 466 4 ss ss NOUN bjmsr-311 466 5 m m ADJ bjmsr-311 466 6 k k NOUN bjmsr-311 466 7 m m VERB bjmsr-311 466 8 kk kk INTJ bjmsr-311 467 1 s s X bjmsr-311 467 2 s s PROPN bjmsr-311 467 3 ss ss NOUN bjmsr-311 467 4 m m NOUN bjmsr-311 467 5 k k NOUN bjmsr-311 467 6 m m VERB bjmsr-311 467 7 k k PROPN bjmsr-311 467 8 kk kk INTJ bjmsr-311 467 9 m m VERB bjmsr-311 467 10 k k NOUN bjmsr-311 467 11 m m VERB bjmsr-311 467 12 kk kk INTJ bjmsr-311 467 13 y y INTJ bjmsr-311 467 14 xy xy PROPN bjmsr-311 467 15 x x PUNCT bjmsr-311 468 1 xy xy NOUN bjmsr-311 468 2 x x PUNCT bjmsr-311 468 3 x x X bjmsr-311 468 4 xy xy PUNCT bjmsr-311 468 5 x x PUNCT bjmsr-311 468 6 xy xy PROPN bjmsr-311 468 7   PROPN bjmsr-311 468 8   PROPN bjmsr-311 468 9   PROPN bjmsr-311 468 10   PROPN bjmsr-311 468 11   PROPN bjmsr-311 468 12   PROPN bjmsr-311 468 13   PROPN bjmsr-311 468 14   PROPN bjmsr-311 468 15   VERB bjmsr-311 468 16   PROPN bjmsr-311 468 17   NOUN bjmsr-311 468 18   PUNCT bjmsr-311 468 19   NOUN bjmsr-311 468 20   PROPN bjmsr-311 468 21   PROPN bjmsr-311 468 22   PROPN bjmsr-311 468 23   PROPN bjmsr-311 468 24   PROPN bjmsr-311 468 25   PROPN bjmsr-311 468 26   PROPN bjmsr-311 468 27   PROPN bjmsr-311 468 28   PROPN bjmsr-311 468 29   NOUN bjmsr-311 468 30   PROPN bjmsr-311 469 1   NOUN bjmsr-311 469 2   PROPN bjmsr-311 470 1   PROPN bjmsr-311 471 1   PROPN bjmsr-311 472 1   PROPN bjmsr-311 473 1   INTJ bjmsr-311 474 1   PROPN bjmsr-311 475 1   INTJ bjmsr-311 476 1   PROPN bjmsr-311 477 1   INTJ bjmsr-311 478 1   PROPN bjmsr-311 479 1   INTJ bjmsr-311 480 1   PROPN bjmsr-311 480 2   PROPN bjmsr-311 481 1   NUM bjmsr-311 481 2   PROPN bjmsr-311 481 3   PROPN bjmsr-311 482 1   PROPN bjmsr-311 483 1   INTJ bjmsr-311 484 1   PROPN bjmsr-311 485 1   INTJ bjmsr-311 486 1   PROPN bjmsr-311 487 1   INTJ bjmsr-311 488 1   PROPN bjmsr-311 489 1   INTJ bjmsr-311 490 1   PROPN bjmsr-311 491 1   INTJ bjmsr-311 492 1   PROPN bjmsr-311 493 1   INTJ bjmsr-311 494 1   PROPN bjmsr-311 495 1   INTJ bjmsr-311 495 2   PROPN bjmsr-311 495 3   NOUN bjmsr-311 496 1   PROPN bjmsr-311 497 1   ADJ bjmsr-311 497 2   NOUN bjmsr-311 497 3   NOUN bjmsr-311 497 4 1 1 NUM bjmsr-311 497 5 2 2 NUM bjmsr-311 497 6 2 2 NUM bjmsr-311 497 7 1 1 NUM bjmsr-311 497 8 1 1 NUM bjmsr-311 497 9 2 2 NUM bjmsr-311 497 10 1 1 NUM bjmsr-311 497 11 1 1 NUM bjmsr-311 497 12 1 1 NUM bjmsr-311 497 13 0 0 NUM bjmsr-311 497 14 0 0 NUM bjmsr-311 497 15 m m VERB bjmsr-311 497 16 m m VERB bjmsr-311 497 17 k k ADJ bjmsr-311 498 1 kx kx PROPN bjmsr-311 498 2 x x PUNCT bjmsr-311 498 3   PROPN bjmsr-311 498 4   PROPN bjmsr-311 498 5   PROPN bjmsr-311 498 6   PROPN bjmsr-311 498 7   PROPN bjmsr-311 498 8   NOUN bjmsr-311 498 9   PROPN bjmsr-311 498 10   PROPN bjmsr-311 498 11   PROPN bjmsr-311 498 12   PROPN bjmsr-311 498 13   NOUN bjmsr-311 498 14   PROPN bjmsr-311 498 15   PROPN bjmsr-311 498 16   PROPN bjmsr-311 499 1   NOUN bjmsr-311 500 1   PROPN bjmsr-311 500 2   PROPN bjmsr-311 500 3   NOUN bjmsr-311 501 1   PROPN bjmsr-311 501 2   PROPN bjmsr-311 501 3   NOUN bjmsr-311 502 1   PROPN bjmsr-311 502 2   PROPN bjmsr-311 502 3   NOUN bjmsr-311 503 1   PROPN bjmsr-311 503 2   PROPN bjmsr-311 503 3   NOUN bjmsr-311 504 1   PROPN bjmsr-311 504 2   PROPN bjmsr-311 504 3   NOUN bjmsr-311 505 1   PROPN bjmsr-311 505 2   PROPN bjmsr-311 505 3   NOUN bjmsr-311 506 1   PROPN bjmsr-311 506 2   PROPN bjmsr-311 506 3   NOUN bjmsr-311 507 1   PROPN bjmsr-311 508 1   ADJ bjmsr-311 508 2   NOUN bjmsr-311 508 3   NOUN bjmsr-311 508 4 ( ( PUNCT bjmsr-311 508 5 96 96 NUM bjmsr-311 508 6 ) ) PUNCT bjmsr-311 508 7 the the DET bjmsr-311 508 8 recursive recursive ADJ bjmsr-311 508 9 system system NOUN bjmsr-311 508 10 of of ADP bjmsr-311 508 11 equations equation NOUN bjmsr-311 508 12 ( ( PUNCT bjmsr-311 508 13 96 96 NUM bjmsr-311 508 14 ) ) PUNCT bjmsr-311 508 15 can can AUX bjmsr-311 508 16 be be AUX bjmsr-311 508 17 obtained obtain VERB bjmsr-311 508 18 as as ADP bjmsr-311 508 19 follows follow VERB bjmsr-311 508 20 . . PUNCT bjmsr-311 509 1 solve solve VERB bjmsr-311 509 2 ( ( PUNCT bjmsr-311 509 3 67 67 NUM bjmsr-311 509 4 ) ) PUNCT bjmsr-311 509 5 and and CCONJ bjmsr-311 509 6 ( ( PUNCT bjmsr-311 509 7 68 68 NUM bjmsr-311 509 8 ) ) PUNCT bjmsr-311 509 9 for for ADP bjmsr-311 509 10 y y PROPN bjmsr-311 509 11 i i PROPN bjmsr-311 509 12 and and CCONJ bjmsr-311 509 13 xji xji PROPN bjmsr-311 509 14 , , PUNCT bjmsr-311 509 15 j=1,2,3 j=1,2,3 NUM bjmsr-311 509 16 ; ; PUNCT bjmsr-311 509 17 and and CCONJ bjmsr-311 509 18 substitute substitute VERB bjmsr-311 509 19 them they PRON bjmsr-311 509 20 into into ADP bjmsr-311 509 21 ( ( PUNCT bjmsr-311 509 22 66 66 NUM bjmsr-311 509 23 ) ) PUNCT bjmsr-311 509 24 , , PUNCT bjmsr-311 509 25 gives give VERB bjmsr-311 509 26 n n PRON bjmsr-311 509 27 sk1 sk1 PROPN bjmsr-311 509 28 = = PROPN bjmsr-311 509 29 σ σ PROPN bjmsr-311 509 30 │ │ NOUN bjmsr-311 509 31 yi yi PROPN bjmsr-311 509 32 k1 k1 PROPN bjmsr-311 509 33 - - PUNCT bjmsr-311 509 34 ß1x1i ß1x1i NUM bjmsr-311 509 35 k1 k1 PROPN bjmsr-311 509 36 - - PUNCT bjmsr-311 509 37 ß2x2i ß2x2i NUM bjmsr-311 509 38 k1 k1 NOUN bjmsr-311 509 39 - - PUNCT bjmsr-311 509 40 ß3x3i ß3x3i NOUN bjmsr-311 509 41 k1-(yk1 k1-(yk1 PROPN bjmsr-311 509 42 - - PUNCT bjmsr-311 509 43 ß0 ß0 NOUN bjmsr-311 509 44 - - PUNCT bjmsr-311 509 45 ß1x2k1 ß1x2k1 NOUN bjmsr-311 509 46 - - PUNCT bjmsr-311 509 47 ß3x3k1 ß3x3k1 NOUN bjmsr-311 509 48 ) ) PUNCT bjmsr-311 509 49 │ │ X bjmsr-311 509 50 ( ( PUNCT bjmsr-311 509 51 97 97 NUM bjmsr-311 509 52 ) ) PUNCT bjmsr-311 509 53 i=1 i=1 PROPN bjmsr-311 509 54 since since SCONJ bjmsr-311 509 55 we we PRON bjmsr-311 509 56 force force VERB bjmsr-311 509 57 the the DET bjmsr-311 509 58 regression regression NOUN bjmsr-311 509 59 to to PART bjmsr-311 509 60 pass pass VERB bjmsr-311 509 61 through through ADP bjmsr-311 509 62 the the DET bjmsr-311 509 63 point point NOUN bjmsr-311 509 64 k1 k1 NOUN bjmsr-311 509 65 , , PUNCT bjmsr-311 509 66 the the DET bjmsr-311 509 67 expression expression NOUN bjmsr-311 509 68 inside inside ADP bjmsr-311 509 69 the the DET bjmsr-311 509 70 parentheses parenthesis NOUN bjmsr-311 509 71 of of ADP bjmsr-311 509 72 ( ( PUNCT bjmsr-311 509 73 97 97 NUM bjmsr-311 509 74 ) ) PUNCT bjmsr-311 509 75 is be AUX bjmsr-311 509 76 equal equal ADJ bjmsr-311 509 77 to to ADP bjmsr-311 509 78 zero zero NUM bjmsr-311 509 79 . . PUNCT bjmsr-311 510 1 hence hence ADV bjmsr-311 510 2 , , PUNCT bjmsr-311 510 3 yk1 yk1 NOUN bjmsr-311 510 4 - - PUNCT bjmsr-311 510 5 ß0 ß0 NOUN bjmsr-311 510 6 - - PUNCT bjmsr-311 510 7 ß1x2k1 ß1x2k1 NOUN bjmsr-311 510 8 - - PUNCT bjmsr-311 510 9 ß3x3k1 ß3x3k1 NOUN bjmsr-311 510 10 = = NOUN bjmsr-311 510 11 0 0 NUM bjmsr-311 510 12 ( ( PUNCT bjmsr-311 510 13 98 98 NUM bjmsr-311 510 14 ) ) PUNCT bjmsr-311 510 15 we we PRON bjmsr-311 510 16 can can AUX bjmsr-311 510 17 solve solve VERB bjmsr-311 510 18 ( ( PUNCT bjmsr-311 510 19 73 73 NUM bjmsr-311 510 20 ) ) PUNCT bjmsr-311 510 21 and and CCONJ bjmsr-311 510 22 ( ( PUNCT bjmsr-311 510 23 74 74 NUM bjmsr-311 510 24 ) ) PUNCT bjmsr-311 510 25 again again ADV bjmsr-311 510 26 for for ADP bjmsr-311 510 27 yi yi PROPN bjmsr-311 510 28 s1 s1 PROPN bjmsr-311 510 29 and and CCONJ bjmsr-311 510 30 xji xji NUM bjmsr-311 510 31 s1 s1 NOUN bjmsr-311 510 32 , , PUNCT bjmsr-311 510 33 where where SCONJ bjmsr-311 510 34 , , PUNCT bjmsr-311 510 35 j=2,3 j=2,3 NOUN bjmsr-311 510 36 and and CCONJ bjmsr-311 510 37 substitute substitute VERB bjmsr-311 510 38 them they PRON bjmsr-311 510 39 into into ADP bjmsr-311 510 40 ( ( PUNCT bjmsr-311 510 41 72 72 NUM bjmsr-311 510 42 ) ) PUNCT bjmsr-311 510 43 which which PRON bjmsr-311 510 44 leads lead VERB bjmsr-311 510 45 to to ADP bjmsr-311 510 46 the the DET bjmsr-311 510 47 following follow VERB bjmsr-311 510 48 objective objective ADJ bjmsr-311 510 49 function function NOUN bjmsr-311 510 50 , , PUNCT bjmsr-311 510 51 n n CCONJ bjmsr-311 510 52 sk1k2 sk1k2 PROPN bjmsr-311 510 53 = = PROPN bjmsr-311 510 54 σ σ PROPN bjmsr-311 510 55 │ │ PROPN bjmsr-311 510 56 x1i x1i PROPN bjmsr-311 510 57 k1 k1 NOUN bjmsr-311 510 58 │ │ VERB bjmsr-311 510 59 │ │ NOUN bjmsr-311 510 60 yi yi NOUN bjmsr-311 510 61 k2 k2 PROPN bjmsr-311 510 62 - - PUNCT bjmsr-311 510 63 ß2x2i ß2x2i NOUN bjmsr-311 510 64 k2 k2 PROPN bjmsr-311 510 65 - - PUNCT bjmsr-311 510 66 ß3x3i ß3x3i X bjmsr-311 510 67 k2-(yk2 k2-(yk2 PROPN bjmsr-311 510 68 s1 s1 PROPN bjmsr-311 510 69 - - PUNCT bjmsr-311 510 70 ß1 ß1 NOUN bjmsr-311 510 71 - - PUNCT bjmsr-311 510 72 ß2x2k2 ß2x2k2 NOUN bjmsr-311 510 73 s1 s1 NOUN bjmsr-311 510 74 - - PUNCT bjmsr-311 510 75 ß3x3k2 ß3x3k2 NOUN bjmsr-311 510 76 s1 s1 NOUN bjmsr-311 510 77 ) ) PUNCT bjmsr-311 510 78 │ │ X bjmsr-311 510 79 ( ( PUNCT bjmsr-311 510 80 99 99 NUM bjmsr-311 510 81 ) ) PUNCT bjmsr-311 510 82 i=1 i=1 NOUN bjmsr-311 510 83 by by ADP bjmsr-311 510 84 a a DET bjmsr-311 510 85 similar similar ADJ bjmsr-311 510 86 discussion discussion NOUN bjmsr-311 510 87 on on ADP bjmsr-311 510 88 ( ( PUNCT bjmsr-311 510 89 97 97 NUM bjmsr-311 510 90 ) ) PUNCT bjmsr-311 510 91 we we PRON bjmsr-311 510 92 have have VERB bjmsr-311 510 93 , , PUNCT bjmsr-311 511 1 yk2 yk2 VERB bjmsr-311 511 2 s1 s1 NOUN bjmsr-311 511 3 - - PUNCT bjmsr-311 511 4 ß1 ß1 NOUN bjmsr-311 511 5 - - PUNCT bjmsr-311 511 6 ß2x2k2 ß2x2k2 NOUN bjmsr-311 511 7 s1 s1 NOUN bjmsr-311 511 8 - - PUNCT bjmsr-311 511 9 ß3x3k2 ß3x3k2 NOUN bjmsr-311 511 10 s1 s1 NOUN bjmsr-311 511 11 = = SYM bjmsr-311 511 12 0 0 NUM bjmsr-311 511 13 ( ( PUNCT bjmsr-311 511 14 100 100 NUM bjmsr-311 511 15 ) ) PUNCT bjmsr-311 511 16 similarly similarly ADV bjmsr-311 511 17 we we PRON bjmsr-311 511 18 can can AUX bjmsr-311 511 19 derive derive VERB bjmsr-311 511 20 , , PUNCT bjmsr-311 511 21 n n NOUN bjmsr-311 512 1 sk1k2k3 sk1k2k3 PROPN bjmsr-311 512 2 = = PROPN bjmsr-311 512 3 σ σ PROPN bjmsr-311 512 4 │ │ PROPN bjmsr-311 512 5 x1i x1i PROPN bjmsr-311 512 6 k1x2i k1x2i PUNCT bjmsr-311 512 7 k2 k2 X bjmsr-311 512 8 │ │ VERB bjmsr-311 512 9 │ │ NOUN bjmsr-311 512 10 yi yi NOUN bjmsr-311 512 11 k3 k3 PROPN bjmsr-311 512 12 - - PUNCT bjmsr-311 512 13 ß3x3i ß3x3i X bjmsr-311 512 14 k3+(yk3 k3+(yk3 PROPN bjmsr-311 512 15 s2 s2 PROPN bjmsr-311 512 16 - - PUNCT bjmsr-311 512 17 ß2 ß2 VERB bjmsr-311 512 18 - - PUNCT bjmsr-311 512 19 ß3x3k3 ß3x3k3 NOUN bjmsr-311 512 20 s2 s2 PROPN bjmsr-311 512 21 ) ) PUNCT bjmsr-311 512 22 │ │ X bjmsr-311 512 23 ( ( PUNCT bjmsr-311 512 24 101 101 NUM bjmsr-311 512 25 ) ) PUNCT bjmsr-311 512 26 i=1 i=1 PROPN bjmsr-311 512 27 and and CCONJ bjmsr-311 512 28 based base VERB bjmsr-311 512 29 on on ADP bjmsr-311 512 30 ( ( PUNCT bjmsr-311 512 31 101 101 NUM bjmsr-311 512 32 ) ) PUNCT bjmsr-311 512 33 , , PUNCT bjmsr-311 512 34 yk3 yk3 PROPN bjmsr-311 512 35 s2 s2 PROPN bjmsr-311 512 36 - - PUNCT bjmsr-311 512 37 ß2 ß2 VERB bjmsr-311 512 38 - - PUNCT bjmsr-311 512 39 ß3x3k3 ß3x3k3 NOUN bjmsr-311 512 40 s2 s2 NOUN bjmsr-311 512 41 = = SYM bjmsr-311 512 42 0 0 PUNCT bjmsr-311 512 43 ( ( PUNCT bjmsr-311 512 44 102 102 NUM bjmsr-311 512 45 ) ) PUNCT bjmsr-311 512 46 finally finally ADV bjmsr-311 512 47 , , PUNCT bjmsr-311 512 48 by by ADP bjmsr-311 512 49 solving solve VERB bjmsr-311 512 50 the the DET bjmsr-311 512 51 weighted weight VERB bjmsr-311 512 52 median median ADJ bjmsr-311 512 53 problem problem NOUN bjmsr-311 512 54 ( ( PUNCT bjmsr-311 512 55 83 83 NUM bjmsr-311 512 56 ) ) PUNCT bjmsr-311 512 57 , , PUNCT bjmsr-311 512 58 we we PRON bjmsr-311 512 59 find find VERB bjmsr-311 512 60 a a DET bjmsr-311 512 61 point point NOUN bjmsr-311 512 62 m m VERB bjmsr-311 512 63 which which PRON bjmsr-311 512 64 gives give VERB bjmsr-311 512 65 , , PUNCT bjmsr-311 512 66 ß3 ß3 NOUN bjmsr-311 512 67 = = PROPN bjmsr-311 512 68 ym ym PROPN bjmsr-311 512 69 s3 s3 PROPN bjmsr-311 512 70 ( ( PUNCT bjmsr-311 512 71 103 103 NUM bjmsr-311 512 72 ) ) PUNCT bjmsr-311 512 73 equations equation NOUN bjmsr-311 512 74 ( ( PUNCT bjmsr-311 512 75 103 103 NUM bjmsr-311 512 76 ) ) PUNCT bjmsr-311 512 77 , , PUNCT bjmsr-311 512 78 ( ( PUNCT bjmsr-311 512 79 102 102 NUM bjmsr-311 512 80 ) ) PUNCT bjmsr-311 512 81 , , PUNCT bjmsr-311 512 82 ( ( PUNCT bjmsr-311 512 83 100 100 NUM bjmsr-311 512 84 ) ) PUNCT bjmsr-311 512 85 and and CCONJ bjmsr-311 512 86 ( ( PUNCT bjmsr-311 512 87 98 98 NUM bjmsr-311 512 88 ) ) PUNCT bjmsr-311 512 89 can can AUX bjmsr-311 512 90 be be AUX bjmsr-311 512 91 solved solve VERB bjmsr-311 512 92 sequentially sequentially ADV bjmsr-311 512 93 for for ADP bjmsr-311 512 94 ß3^, ß3^, NOUN bjmsr-311 512 95 ... ... PUNCT bjmsr-311 512 96 ,ß0^. ,ß0^. PUNCT bjmsr-311 512 97 in in ADP bjmsr-311 512 98 a a DET bjmsr-311 512 99 similar similar ADJ bjmsr-311 512 100 fashion fashion NOUN bjmsr-311 512 101 , , PUNCT bjmsr-311 512 102 the the DET bjmsr-311 512 103 general general ADJ bjmsr-311 512 104 solution solution NOUN bjmsr-311 512 105 for for ADP bjmsr-311 512 106 m m PROPN bjmsr-311 512 107 parameters parameter NOUN bjmsr-311 512 108 model model NOUN bjmsr-311 512 109 is be AUX bjmsr-311 512 110 given give VERB bjmsr-311 512 111 by by ADP bjmsr-311 512 112 ( ( PUNCT bjmsr-311 512 113 96 96 NUM bjmsr-311 512 114 ) ) PUNCT bjmsr-311 512 115 . . PUNCT bjmsr-311 513 1 now now ADV bjmsr-311 513 2 let let VERB bjmsr-311 513 3 us we PRON bjmsr-311 513 4 use use VERB bjmsr-311 513 5 these these DET bjmsr-311 513 6 properties property NOUN bjmsr-311 513 7 and and CCONJ bjmsr-311 513 8 give give VERB bjmsr-311 513 9 the the DET bjmsr-311 513 10 computational computational ADJ bjmsr-311 513 11 steps step NOUN bjmsr-311 513 12 of of ADP bjmsr-311 513 13 algorithm algorithm NOUN bjmsr-311 513 14 4 4 NUM bjmsr-311 513 15 more more ADJ bjmsr-311 513 16 expository expository NOUN bjmsr-311 513 17 in in ADP bjmsr-311 513 18 the the DET bjmsr-311 513 19 following follow VERB bjmsr-311 513 20 bl1 bl1 NOUN bjmsr-311 513 21 program program NOUN bjmsr-311 513 22 . . PUNCT bjmsr-311 514 1 program program NOUN bjmsr-311 514 2 bl1 bl1 NOUN bjmsr-311 514 3 step step NOUN bjmsr-311 514 4 0 0 NUM bjmsr-311 514 5 ) ) PUNCT bjmsr-311 514 6 initialization initialization NOUN bjmsr-311 514 7 . . PUNCT bjmsr-311 515 1 parameter parameter NOUN bjmsr-311 515 2 : : PUNCT bjmsr-311 515 3 n n CCONJ bjmsr-311 515 4 , , PUNCT bjmsr-311 515 5 m m PROPN bjmsr-311 515 6 , , PUNCT bjmsr-311 515 7 m1 m1 PROPN bjmsr-311 515 8 = = SYM bjmsr-311 515 9 m-1 m-1 PROPN bjmsr-311 515 10 , , PUNCT bjmsr-311 515 11 m2 m2 PROPN bjmsr-311 515 12 = = NOUN bjmsr-311 515 13 m-2 m-2 NOUN bjmsr-311 515 14 . . PUNCT bjmsr-311 516 1 real real ADJ bjmsr-311 516 2 : : PUNCT bjmsr-311 516 3 y(n y(n PROPN bjmsr-311 516 4 ) ) PUNCT bjmsr-311 516 5 , , PUNCT bjmsr-311 516 6 x(n x(n PROPN bjmsr-311 516 7 , , PUNCT bjmsr-311 516 8 m1 m1 NOUN bjmsr-311 516 9 ) ) PUNCT bjmsr-311 516 10 , , PUNCT bjmsr-311 516 11 xsk(m1 xsk(m1 PROPN bjmsr-311 516 12 ) ) PUNCT bjmsr-311 516 13 , , PUNCT bjmsr-311 516 14 yw(n yw(n PROPN bjmsr-311 516 15 ) ) PUNCT bjmsr-311 516 16 , , PUNCT bjmsr-311 516 17 xkw(n xkw(n PROPN bjmsr-311 516 18 ) ) PUNCT bjmsr-311 516 19 , , PUNCT bjmsr-311 516 20 w(n w(n PROPN bjmsr-311 516 21 ) ) PUNCT bjmsr-311 516 22 , , PUNCT bjmsr-311 516 23 ys(n ys(n NUM bjmsr-311 516 24 ) ) PUNCT bjmsr-311 516 25 , , PUNCT bjmsr-311 516 26 xs(n xs(n PROPN bjmsr-311 516 27 , , PUNCT bjmsr-311 516 28 m1 m1 NOUN bjmsr-311 516 29 ) ) PUNCT bjmsr-311 516 30 , , PUNCT bjmsr-311 516 31 b(m b(m PROPN bjmsr-311 516 32 ) ) PUNCT bjmsr-311 516 33 , , PUNCT bjmsr-311 516 34 xw(n,2 xw(n,2 PROPN bjmsr-311 516 35 : : PUNCT bjmsr-311 516 36 m1 m1 NOUN bjmsr-311 516 37 ) ) PUNCT bjmsr-311 516 38 , , PUNCT bjmsr-311 516 39 ysol(m1 ysol(m1 NOUN bjmsr-311 516 40 ) ) PUNCT bjmsr-311 516 41 , , PUNCT bjmsr-311 516 42 xsol(m1,m1 xsol(m1,m1 PROPN bjmsr-311 516 43 ) ) PUNCT bjmsr-311 516 44 . . PUNCT bjmsr-311 517 1 integer integer NOUN bjmsr-311 517 2 : : PUNCT bjmsr-311 517 3 l(n l(n PROPN bjmsr-311 517 4 ) ) PUNCT bjmsr-311 517 5 , , PUNCT bjmsr-311 517 6 kk(m1 kk(m1 PROPN bjmsr-311 517 7 ) ) PUNCT bjmsr-311 517 8 . . PUNCT bjmsr-311 518 1 common common ADJ bjmsr-311 518 2 : : PUNCT bjmsr-311 518 3 /c1 /c1 PROPN bjmsr-311 518 4 / / SYM bjmsr-311 518 5 i1,i2 i1,i2 PROPN bjmsr-311 518 6 . . PUNCT bjmsr-311 519 1 read read VERB bjmsr-311 519 2 : : PUNCT bjmsr-311 519 3 ( ( PUNCT bjmsr-311 519 4 y(i),(x(i y(i),(x(i PROPN bjmsr-311 519 5 , , PUNCT bjmsr-311 519 6 j),j=1,m1),i=1,n j),j=1,m1),i=1,n NOUN bjmsr-311 519 7 ) ) PUNCT bjmsr-311 519 8 . . PUNCT bjmsr-311 520 1 copyright copyright NOUN bjmsr-311 520 2 © © PROPN bjmsr-311 520 3 cc cc PROPN bjmsr-311 520 4 - - PUNCT bjmsr-311 520 5 by by ADP bjmsr-311 520 6 - - PUNCT bjmsr-311 520 7 nc nc PROPN bjmsr-311 520 8 2019 2019 NUM bjmsr-311 520 9 , , PUNCT bjmsr-311 520 10 bjmsr bjmsr PROPN bjmsr-311 520 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 521 1 bangladesh bangladesh PROPN bjmsr-311 521 2 journal journal PROPN bjmsr-311 521 3 of of ADP bjmsr-311 521 4 multidisciplinary multidisciplinary ADJ bjmsr-311 521 5 scientific scientific ADJ bjmsr-311 521 6 research research NOUN bjmsr-311 521 7 vol vol NOUN bjmsr-311 521 8 . . PROPN bjmsr-311 521 9 1 1 NUM bjmsr-311 521 10 , , PUNCT bjmsr-311 521 11 no no INTJ bjmsr-311 521 12 . . NOUN bjmsr-311 521 13 1 1 NUM bjmsr-311 521 14 ; ; PUNCT bjmsr-311 521 15 2019 2019 NUM bjmsr-311 521 16 16 16 NUM bjmsr-311 521 17 let let VERB bjmsr-311 521 18 : : PUNCT bjmsr-311 521 19 iter=0 iter=0 ADV bjmsr-311 521 20 , , PUNCT bjmsr-311 521 21 kr=0 kr=0 ADJ bjmsr-311 521 22 , , PUNCT bjmsr-311 521 23 mm=1 mm=1 PROPN bjmsr-311 521 24 , , PUNCT bjmsr-311 521 25 ( ( PUNCT bjmsr-311 521 26 kk(j)=arbitrary kk(j)=arbitrary PROPN bjmsr-311 521 27 , , PUNCT bjmsr-311 521 28 j=1,m1 j=1,m1 PROPN bjmsr-311 521 29 ) ) PUNCT bjmsr-311 521 30 . . PUNCT bjmsr-311 522 1 step step NOUN bjmsr-311 522 2 1 1 NUM bjmsr-311 522 3 ) ) PUNCT bjmsr-311 522 4 refill refill NOUN bjmsr-311 522 5 working working NOUN bjmsr-311 522 6 arrays array VERB bjmsr-311 522 7 . . PUNCT bjmsr-311 523 1 do do AUX bjmsr-311 523 2 loop loop VERB bjmsr-311 523 3 for for ADP bjmsr-311 523 4 i=1,n i=1,n NOUN bjmsr-311 523 5 : : PUNCT bjmsr-311 523 6 ys(i)=y(i ys(i)=y(i NOUN bjmsr-311 523 7 ) ) PUNCT bjmsr-311 523 8 , , PUNCT bjmsr-311 523 9 do do AUX bjmsr-311 523 10 loop loop VERB bjmsr-311 523 11 for for ADP bjmsr-311 523 12 j=1,m1 j=1,m1 PROPN bjmsr-311 523 13 : : PUNCT bjmsr-311 523 14 xs(i xs(i NUM bjmsr-311 523 15 , , PUNCT bjmsr-311 523 16 j)=x(i j)=x(i PROPN bjmsr-311 523 17 , , PUNCT bjmsr-311 523 18 j j PROPN bjmsr-311 523 19 ) ) PUNCT bjmsr-311 523 20 , , PUNCT bjmsr-311 523 21 end end NOUN bjmsr-311 523 22 do do AUX bjmsr-311 523 23 , , PUNCT bjmsr-311 523 24 end end VERB bjmsr-311 523 25 do do AUX bjmsr-311 523 26 . . PUNCT bjmsr-311 524 1 step step VERB bjmsr-311 524 2 2 2 NUM bjmsr-311 524 3 ) ) PUNCT bjmsr-311 524 4 store store NOUN bjmsr-311 524 5 weights weight NOUN bjmsr-311 524 6 and and CCONJ bjmsr-311 524 7 ratios ratio NOUN bjmsr-311 524 8 for for ADP bjmsr-311 524 9 next next ADJ bjmsr-311 524 10 iteration iteration NOUN bjmsr-311 524 11 . . PUNCT bjmsr-311 525 1 do do AUX bjmsr-311 525 2 loop loop VERB bjmsr-311 525 3 for for ADP bjmsr-311 525 4 i=1,n i=1,n NOUN bjmsr-311 525 5 : : PUNCT bjmsr-311 525 6 w(i)=xkw(i w(i)=xkw(i PROPN bjmsr-311 525 7 ) ) PUNCT bjmsr-311 525 8 , , PUNCT bjmsr-311 525 9 ys(i)=yw(i ys(i)=yw(i NOUN bjmsr-311 525 10 ) ) PUNCT bjmsr-311 525 11 , , PUNCT bjmsr-311 525 12 do do AUX bjmsr-311 525 13 loop loop VERB bjmsr-311 525 14 for for ADP bjmsr-311 525 15 j=1,m1 j=1,m1 PROPN bjmsr-311 525 16 : : PUNCT bjmsr-311 525 17 xs(i xs(i NUM bjmsr-311 525 18 , , PUNCT bjmsr-311 525 19 j)=xw(i j)=xw(i PROPN bjmsr-311 525 20 , , PUNCT bjmsr-311 525 21 j j PROPN bjmsr-311 525 22 ) ) PUNCT bjmsr-311 525 23 , , PUNCT bjmsr-311 525 24 end end NOUN bjmsr-311 525 25 do do AUX bjmsr-311 525 26 , , PUNCT bjmsr-311 525 27 end end VERB bjmsr-311 525 28 do do AUX bjmsr-311 525 29 . . PUNCT bjmsr-311 526 1 step step VERB bjmsr-311 526 2 3 3 NUM bjmsr-311 526 3 ) ) PUNCT bjmsr-311 526 4 compute compute VERB bjmsr-311 526 5 the the DET bjmsr-311 526 6 arguments argument NOUN bjmsr-311 526 7 for for ADP bjmsr-311 526 8 weighted weight VERB bjmsr-311 526 9 median median PROPN bjmsr-311 526 10 . . PUNCT bjmsr-311 527 1 a. a. PROPN bjmsr-311 527 2 set set PROPN bjmsr-311 527 3 : : PUNCT bjmsr-311 528 1 jj jj PROPN bjmsr-311 528 2 = = PROPN bjmsr-311 528 3 mm mm PROPN bjmsr-311 528 4 , , PUNCT bjmsr-311 528 5 k k NOUN bjmsr-311 528 6 = = NOUN bjmsr-311 528 7 kk(jj kk(jj NOUN bjmsr-311 528 8 ) ) PUNCT bjmsr-311 528 9 , , PUNCT bjmsr-311 528 10 ysk ysk NOUN bjmsr-311 528 11 = = NOUN bjmsr-311 528 12 ys(k ys(k NUM bjmsr-311 528 13 ) ) PUNCT bjmsr-311 528 14 , , PUNCT bjmsr-311 528 15 i1=1 i1=1 PROPN bjmsr-311 528 16 , , PUNCT bjmsr-311 528 17 i2 i2 PROPN bjmsr-311 528 18 = = PROPN bjmsr-311 528 19 k-1 k-1 PROPN bjmsr-311 528 20 . . PUNCT bjmsr-311 529 1 do do AUX bjmsr-311 529 2 loop loop VERB bjmsr-311 529 3 for for ADP bjmsr-311 529 4 j j PROPN bjmsr-311 529 5 = = PROPN bjmsr-311 529 6 jj jj PROPN bjmsr-311 529 7 , , PUNCT bjmsr-311 529 8 m1 m1 NOUN bjmsr-311 529 9 : : PUNCT bjmsr-311 529 10 xsk(j)=xs(k xsk(j)=xs(k PROPN bjmsr-311 529 11 , , PUNCT bjmsr-311 529 12 j j PROPN bjmsr-311 529 13 ) ) PUNCT bjmsr-311 529 14 , , PUNCT bjmsr-311 529 15 end end NOUN bjmsr-311 529 16 do do AUX bjmsr-311 529 17 . . PUNCT bjmsr-311 530 1 b. b. PROPN bjmsr-311 530 2 do do AUX bjmsr-311 530 3 loop loop VERB bjmsr-311 530 4 for for ADP bjmsr-311 530 5 j j PROPN bjmsr-311 530 6 = = PROPN bjmsr-311 530 7 jj jj PROPN bjmsr-311 530 8 , , PUNCT bjmsr-311 530 9 m1 m1 NOUN bjmsr-311 530 10 : : PUNCT bjmsr-311 530 11 call call VERB bjmsr-311 530 12 col1(xsk(j),xs(1,j col1(xsk(j),xs(1,j NOUN bjmsr-311 530 13 ) ) PUNCT bjmsr-311 530 14 ) ) PUNCT bjmsr-311 531 1 end end NOUN bjmsr-311 531 2 do do VERB bjmsr-311 531 3 . . PUNCT bjmsr-311 532 1 call call VERB bjmsr-311 532 2 col2(ysk col2(ysk NOUN bjmsr-311 532 3 , , PUNCT bjmsr-311 532 4 jj jj PROPN bjmsr-311 532 5 , , PUNCT bjmsr-311 532 6 w w PROPN bjmsr-311 532 7 , , PUNCT bjmsr-311 532 8 ys ys NOUN bjmsr-311 532 9 , , PUNCT bjmsr-311 532 10 xs(1,jj xs(1,jj PROPN bjmsr-311 532 11 ) ) PUNCT bjmsr-311 532 12 ) ) PUNCT bjmsr-311 532 13 . . PUNCT bjmsr-311 533 1 if if SCONJ bjmsr-311 533 2 i2 i2 PROPN bjmsr-311 533 3 = = NOUN bjmsr-311 533 4 n n PRON bjmsr-311 533 5 go go VERB bjmsr-311 533 6 to to PART bjmsr-311 533 7 step step VERB bjmsr-311 533 8 3.c 3.c NUM bjmsr-311 533 9 ; ; PUNCT bjmsr-311 533 10 otherwise otherwise ADV bjmsr-311 533 11 set set VERB bjmsr-311 533 12 : : PUNCT bjmsr-311 533 13 i1 i1 PROPN bjmsr-311 533 14 = = SYM bjmsr-311 533 15 k+1 k+1 PROPN bjmsr-311 533 16 , , PUNCT bjmsr-311 533 17 i2 i2 PROPN bjmsr-311 533 18 = = SYM bjmsr-311 533 19 n n NUM bjmsr-311 533 20 , , PUNCT bjmsr-311 533 21 go go VERB bjmsr-311 533 22 to to PART bjmsr-311 533 23 step step VERB bjmsr-311 533 24 3.b 3.b NUM bjmsr-311 533 25 . . PUNCT bjmsr-311 534 1 c. c. PROPN bjmsr-311 534 2 set set PROPN bjmsr-311 534 3 : : PUNCT bjmsr-311 534 4 w(k)=0 w(k)=0 ADJ bjmsr-311 534 5 . . PUNCT bjmsr-311 535 1 if if SCONJ bjmsr-311 535 2 jj jj PROPN bjmsr-311 535 3 = = PROPN bjmsr-311 535 4 m1 m1 PROPN bjmsr-311 535 5 go go VERB bjmsr-311 535 6 to to PART bjmsr-311 535 7 step step VERB bjmsr-311 535 8 4 4 NUM bjmsr-311 535 9 ; ; PUNCT bjmsr-311 535 10 otherwise otherwise ADV bjmsr-311 535 11 i1=1 i1=1 PROPN bjmsr-311 535 12 , , PUNCT bjmsr-311 535 13 i2 i2 PROPN bjmsr-311 535 14 = = SYM bjmsr-311 535 15 k-1 k-1 PROPN bjmsr-311 535 16 , , PUNCT bjmsr-311 535 17 go go VERB bjmsr-311 535 18 to to PART bjmsr-311 535 19 step step VERB bjmsr-311 535 20 3.d 3.d NUM bjmsr-311 535 21 . . PUNCT bjmsr-311 536 1 d. d. PROPN bjmsr-311 536 2 do do AUX bjmsr-311 536 3 loop loop VERB bjmsr-311 536 4 for for ADP bjmsr-311 536 5 j j PROPN bjmsr-311 536 6 = = PRON bjmsr-311 536 7 jj+1,m1 jj+1,m1 PROPN bjmsr-311 536 8 : : PUNCT bjmsr-311 536 9 call call NOUN bjmsr-311 536 10 col3(xs(1,j),xs(1,jj col3(xs(1,j),xs(1,jj NOUN bjmsr-311 536 11 ) ) PUNCT bjmsr-311 536 12 ) ) PUNCT bjmsr-311 536 13 , , PUNCT bjmsr-311 536 14 end end NOUN bjmsr-311 536 15 do do VERB bjmsr-311 536 16 . . PUNCT bjmsr-311 537 1 if if SCONJ bjmsr-311 537 2 i i PRON bjmsr-311 537 3 = = VERB bjmsr-311 537 4 n n PRON bjmsr-311 537 5 go go VERB bjmsr-311 537 6 to to PART bjmsr-311 537 7 step step VERB bjmsr-311 537 8 3.e 3.e NUM bjmsr-311 537 9 ; ; PUNCT bjmsr-311 537 10 otherwise otherwise ADV bjmsr-311 537 11 i1 i1 PROPN bjmsr-311 537 12 = = SYM bjmsr-311 537 13 k+1 k+1 PROPN bjmsr-311 537 14 , , PUNCT bjmsr-311 537 15 i2 i2 PROPN bjmsr-311 537 16 = = SYM bjmsr-311 537 17 n n NUM bjmsr-311 537 18 , , PUNCT bjmsr-311 537 19 go go VERB bjmsr-311 537 20 to to PART bjmsr-311 537 21 step step VERB bjmsr-311 537 22 3.d 3.d NUM bjmsr-311 537 23 . . PUNCT bjmsr-311 538 1 e. e. PROPN bjmsr-311 539 1 if if SCONJ bjmsr-311 539 2 jj≠mm jj≠mm PROPN bjmsr-311 539 3 jj jj PROPN bjmsr-311 539 4 = = NOUN bjmsr-311 539 5 jj+1 jj+1 PROPN bjmsr-311 539 6 , , PUNCT bjmsr-311 539 7 go go VERB bjmsr-311 539 8 to to PART bjmsr-311 539 9 step step VERB bjmsr-311 539 10 3 3 NUM bjmsr-311 539 11 , , PUNCT bjmsr-311 539 12 otherwise otherwise ADV bjmsr-311 539 13 do do AUX bjmsr-311 539 14 loop loop NOUN bjmsr-311 539 15 for for ADP bjmsr-311 539 16 i=1,n i=1,n NOUN bjmsr-311 539 17 : : PUNCT bjmsr-311 539 18 xkw(i)=w(i xkw(i)=w(i PROPN bjmsr-311 539 19 ) ) PUNCT bjmsr-311 539 20 , , PUNCT bjmsr-311 539 21 yw(i)=ys(i yw(i)=ys(i NOUN bjmsr-311 539 22 ) ) PUNCT bjmsr-311 539 23 ; ; PUNCT bjmsr-311 539 24 do do AUX bjmsr-311 539 25 loop loop VERB bjmsr-311 539 26 for for ADP bjmsr-311 539 27 j j NOUN bjmsr-311 539 28 = = PROPN bjmsr-311 539 29 jj+1,m1 jj+1,m1 PROPN bjmsr-311 539 30 : : PUNCT bjmsr-311 539 31 xw(i xw(i PROPN bjmsr-311 539 32 , , PUNCT bjmsr-311 539 33 j)=xs(i j)=xs(i PROPN bjmsr-311 539 34 , , PUNCT bjmsr-311 539 35 j j PROPN bjmsr-311 539 36 ) ) PUNCT bjmsr-311 539 37 , , PUNCT bjmsr-311 539 38 end end NOUN bjmsr-311 539 39 do do AUX bjmsr-311 539 40 ; ; PUNCT bjmsr-311 539 41 end end NOUN bjmsr-311 539 42 do do VERB bjmsr-311 539 43 . . PUNCT bjmsr-311 540 1 set set NOUN bjmsr-311 540 2 : : PUNCT bjmsr-311 541 1 jj jj PROPN bjmsr-311 541 2 = = NOUN bjmsr-311 541 3 jj+1 jj+1 PROPN bjmsr-311 541 4 , , PUNCT bjmsr-311 541 5 go go VERB bjmsr-311 541 6 to to PART bjmsr-311 541 7 step step VERB bjmsr-311 541 8 3 3 NUM bjmsr-311 541 9 . . PUNCT bjmsr-311 542 1 step step NOUN bjmsr-311 542 2 4 4 NUM bjmsr-311 542 3 ) ) PUNCT bjmsr-311 542 4 compute compute VERB bjmsr-311 542 5 the the DET bjmsr-311 542 6 weighted weighted ADJ bjmsr-311 542 7 median median NOUN bjmsr-311 542 8 . . PUNCT bjmsr-311 543 1 set set NOUN bjmsr-311 543 2 : : PUNCT bjmsr-311 543 3 ys(k)=0 ys(k)=0 ADJ bjmsr-311 543 4 , , PUNCT bjmsr-311 543 5 iter iter NOUN bjmsr-311 543 6 = = NOUN bjmsr-311 543 7 iter+1 iter+1 ADJ bjmsr-311 543 8 , , PUNCT bjmsr-311 543 9 lm lm PROPN bjmsr-311 543 10 = = NOUN bjmsr-311 543 11 lwmed(n lwmed(n NOUN bjmsr-311 543 12 , , PUNCT bjmsr-311 543 13 ys ys INTJ bjmsr-311 543 14 , , PUNCT bjmsr-311 543 15 w w NOUN bjmsr-311 543 16 , , PUNCT bjmsr-311 543 17 l l NOUN bjmsr-311 543 18 ) ) PUNCT bjmsr-311 543 19 . . PUNCT bjmsr-311 544 1 step step NOUN bjmsr-311 544 2 5 5 NUM bjmsr-311 544 3 ) ) PUNCT bjmsr-311 544 4 test test NOUN bjmsr-311 544 5 for for ADP bjmsr-311 544 6 optimality optimality NOUN bjmsr-311 544 7 . . PUNCT bjmsr-311 545 1 if if SCONJ bjmsr-311 545 2 lm lm NOUN bjmsr-311 545 3 = = NOUN bjmsr-311 545 4 kr kr NOUN bjmsr-311 545 5 go go VERB bjmsr-311 545 6 to to PART bjmsr-311 545 7 step step VERB bjmsr-311 545 8 5.b 5.b NUM bjmsr-311 545 9 ; ; PUNCT bjmsr-311 545 10 otherwise otherwise ADV bjmsr-311 545 11 iopt=0 iopt=0 X bjmsr-311 545 12 go go VERB bjmsr-311 545 13 to to PART bjmsr-311 545 14 step step NOUN bjmsr-311 545 15 5.a 5.a NUM bjmsr-311 545 16 . . PUNCT bjmsr-311 546 1 a. a. NOUN bjmsr-311 547 1 if if SCONJ bjmsr-311 547 2 mm mm PROPN bjmsr-311 547 3 = = PROPN bjmsr-311 547 4 m1 m1 PROPN bjmsr-311 547 5 set set VERB bjmsr-311 547 6 mm=1 mm=1 PROPN bjmsr-311 547 7 , , PUNCT bjmsr-311 547 8 kr kr PROPN bjmsr-311 547 9 = = SYM bjmsr-311 547 10 kk(mm kk(mm PROPN bjmsr-311 547 11 ) ) PUNCT bjmsr-311 547 12 , , PUNCT bjmsr-311 547 13 kk(mm)=lm kk(mm)=lm X bjmsr-311 547 14 , , PUNCT bjmsr-311 547 15 go go VERB bjmsr-311 547 16 to to PART bjmsr-311 547 17 step step VERB bjmsr-311 547 18 1 1 NUM bjmsr-311 547 19 ; ; PUNCT bjmsr-311 547 20 otherwise otherwise ADV bjmsr-311 547 21 set set VERB bjmsr-311 547 22 mm mm PROPN bjmsr-311 547 23 = = SYM bjmsr-311 547 24 mm+1 mm+1 PROPN bjmsr-311 547 25 , , PUNCT bjmsr-311 547 26 kr kr PROPN bjmsr-311 547 27 = = SYM bjmsr-311 547 28 kk(mm kk(mm PROPN bjmsr-311 547 29 ) ) PUNCT bjmsr-311 547 30 , , PUNCT bjmsr-311 547 31 kk(mm)=lm kk(mm)=lm X bjmsr-311 547 32 , , PUNCT bjmsr-311 547 33 go go VERB bjmsr-311 547 34 to to PART bjmsr-311 547 35 step step VERB bjmsr-311 547 36 2 2 NUM bjmsr-311 548 1 . . PUNCT bjmsr-311 548 2 b. b. PROPN bjmsr-311 548 3 set set PROPN bjmsr-311 548 4 : : PUNCT bjmsr-311 548 5 iopt iopt PROPN bjmsr-311 548 6 = = SYM bjmsr-311 548 7 iopt+1 iopt+1 PROPN bjmsr-311 548 8 . . PUNCT bjmsr-311 549 1 if if SCONJ bjmsr-311 549 2 iopt≠m1 iopt≠m1 NOUN bjmsr-311 549 3 go go VERB bjmsr-311 549 4 to to PART bjmsr-311 549 5 step step VERB bjmsr-311 549 6 5.a 5.a NUM bjmsr-311 549 7 , , PUNCT bjmsr-311 549 8 otherwise otherwise ADV bjmsr-311 549 9 go go VERB bjmsr-311 549 10 to to PART bjmsr-311 549 11 step step VERB bjmsr-311 549 12 6 6 NUM bjmsr-311 549 13 . . PUNCT bjmsr-311 550 1 step step NOUN bjmsr-311 550 2 6 6 NUM bjmsr-311 550 3 ) ) PUNCT bjmsr-311 550 4 compute compute VERB bjmsr-311 550 5 the the DET bjmsr-311 550 6 solution solution NOUN bjmsr-311 550 7 . . PUNCT bjmsr-311 551 1 set set NOUN bjmsr-311 551 2 : : PUNCT bjmsr-311 551 3 b(m)=ys(lm b(m)=ys(lm NOUN bjmsr-311 551 4 ) ) PUNCT bjmsr-311 551 5 . . PUNCT bjmsr-311 552 1 do do AUX bjmsr-311 552 2 loop loop VERB bjmsr-311 552 3 for for ADP bjmsr-311 552 4 i=1,m1 i=1,m1 NOUN bjmsr-311 552 5 : : PUNCT bjmsr-311 552 6 ysol(i)=y(kk(i ysol(i)=y(kk(i NUM bjmsr-311 552 7 ) ) PUNCT bjmsr-311 552 8 ) ) PUNCT bjmsr-311 552 9 ; ; PUNCT bjmsr-311 553 1 do do VERB bjmsr-311 553 2 loop loop NOUN bjmsr-311 553 3 for for ADP bjmsr-311 553 4 j=1,m1 j=1,m1 PROPN bjmsr-311 553 5 : : PUNCT bjmsr-311 553 6 xsol(i xsol(i NUM bjmsr-311 553 7 , , PUNCT bjmsr-311 553 8 j)=x(kk(i),j j)=x(kk(i),j PROPN bjmsr-311 553 9 ) ) PUNCT bjmsr-311 553 10 , , PUNCT bjmsr-311 553 11 end end NOUN bjmsr-311 553 12 do do AUX bjmsr-311 553 13 ; ; PUNCT bjmsr-311 553 14 end end NOUN bjmsr-311 553 15 do do VERB bjmsr-311 553 16 . . PUNCT bjmsr-311 554 1 set set NOUN bjmsr-311 554 2 : : PUNCT bjmsr-311 555 1 jj=1 jj=1 X bjmsr-311 555 2 . . PUNCT bjmsr-311 555 3 a. a. PROPN bjmsr-311 555 4 set set PROPN bjmsr-311 555 5 : : PUNCT bjmsr-311 555 6 ysk ysk NOUN bjmsr-311 555 7 = = SYM bjmsr-311 555 8 ysol(jj ysol(jj PROPN bjmsr-311 555 9 ) ) PUNCT bjmsr-311 555 10 . . PUNCT bjmsr-311 556 1 do do AUX bjmsr-311 556 2 loop loop VERB bjmsr-311 556 3 for for ADP bjmsr-311 556 4 j j PROPN bjmsr-311 556 5 = = PROPN bjmsr-311 556 6 jj jj PROPN bjmsr-311 556 7 , , PUNCT bjmsr-311 556 8 m1 m1 NOUN bjmsr-311 556 9 : : PUNCT bjmsr-311 556 10 xsx(j)=xsol(jj xsx(j)=xsol(jj PROPN bjmsr-311 556 11 , , PUNCT bjmsr-311 556 12 j j NOUN bjmsr-311 556 13 ) ) PUNCT bjmsr-311 556 14 , , PUNCT bjmsr-311 556 15 end end NOUN bjmsr-311 556 16 do do VERB bjmsr-311 556 17 . . PUNCT bjmsr-311 557 1 do do AUX bjmsr-311 557 2 loop loop VERB bjmsr-311 557 3 for for ADP bjmsr-311 557 4 i i PROPN bjmsr-311 557 5 = = PROPN bjmsr-311 557 6 jj jj PROPN bjmsr-311 557 7 , , PUNCT bjmsr-311 557 8 m1 m1 NOUN bjmsr-311 557 9 : : PUNCT bjmsr-311 557 10 if if SCONJ bjmsr-311 557 11 i i PRON bjmsr-311 557 12 = = NOUN bjmsr-311 557 13 jj jj PROPN bjmsr-311 557 14 go go VERB bjmsr-311 557 15 to to PART bjmsr-311 557 16 continue continue VERB bjmsr-311 557 17 ; ; PUNCT bjmsr-311 557 18 otherwise otherwise ADV bjmsr-311 557 19 ysol(i)=ysol(i)-ysk ysol(i)=ysol(i)-ysk AUX bjmsr-311 557 20 , , PUNCT bjmsr-311 557 21 do do AUX bjmsr-311 557 22 loop loop VERB bjmsr-311 557 23 for for ADP bjmsr-311 557 24 j j PROPN bjmsr-311 557 25 = = PROPN bjmsr-311 557 26 jj jj PROPN bjmsr-311 557 27 , , PUNCT bjmsr-311 557 28 m1 m1 NOUN bjmsr-311 557 29 : : PUNCT bjmsr-311 558 1 xsol(i xsol(i NUM bjmsr-311 558 2 , , PUNCT bjmsr-311 558 3 j)=xsol(i j)=xsol(i NOUN bjmsr-311 558 4 , , PUNCT bjmsr-311 558 5 j)-xsk(j j)-xsk(j PROPN bjmsr-311 558 6 ) ) PUNCT bjmsr-311 558 7 , , PUNCT bjmsr-311 558 8 end end NOUN bjmsr-311 558 9 do do AUX bjmsr-311 558 10 ; ; PUNCT bjmsr-311 558 11 set set VERB bjmsr-311 558 12 ysol(i)=ysol(i)/xsol(i ysol(i)=ysol(i)/xsol(i PROPN bjmsr-311 558 13 , , PUNCT bjmsr-311 558 14 jj jj PROPN bjmsr-311 558 15 ) ) PUNCT bjmsr-311 558 16 , , PUNCT bjmsr-311 558 17 continue continue VERB bjmsr-311 558 18 , , PUNCT bjmsr-311 558 19 end end VERB bjmsr-311 558 20 do do VERB bjmsr-311 558 21 . . PUNCT bjmsr-311 559 1 b. b. PROPN bjmsr-311 559 2 do do AUX bjmsr-311 559 3 loop loop VERB bjmsr-311 559 4 for for ADP bjmsr-311 559 5 i i PROPN bjmsr-311 559 6 = = PROPN bjmsr-311 559 7 jj jj PROPN bjmsr-311 559 8 , , PUNCT bjmsr-311 559 9 m1 m1 NOUN bjmsr-311 559 10 : : PUNCT bjmsr-311 559 11 if if SCONJ bjmsr-311 559 12 i i PRON bjmsr-311 559 13 = = NOUN bjmsr-311 559 14 jj jj PROPN bjmsr-311 559 15 go go VERB bjmsr-311 559 16 to to PART bjmsr-311 559 17 continue continue VERB bjmsr-311 559 18 , , PUNCT bjmsr-311 559 19 otherwise otherwise ADV bjmsr-311 559 20 , , PUNCT bjmsr-311 559 21 do do AUX bjmsr-311 559 22 loop loop VERB bjmsr-311 559 23 for for ADP bjmsr-311 559 24 j j NOUN bjmsr-311 559 25 = = PRON bjmsr-311 559 26 jj+1,m1 jj+1,m1 X bjmsr-311 559 27 : : PUNCT bjmsr-311 559 28 xsol(i xsol(i NOUN bjmsr-311 559 29 , , PUNCT bjmsr-311 559 30 j)=xsol(i j)=xsol(i NOUN bjmsr-311 559 31 , , PUNCT bjmsr-311 559 32 j)/xsol(i j)/xsol(i PROPN bjmsr-311 559 33 , , PUNCT bjmsr-311 559 34 jj jj PROPN bjmsr-311 559 35 ) ) PUNCT bjmsr-311 559 36 , , PUNCT bjmsr-311 559 37 end end NOUN bjmsr-311 559 38 do do AUX bjmsr-311 559 39 ; ; PUNCT bjmsr-311 559 40 continue continue VERB bjmsr-311 559 41 ; ; PUNCT bjmsr-311 560 1 end end NOUN bjmsr-311 560 2 do do NOUN bjmsr-311 560 3 . . PUNCT bjmsr-311 561 1 c. c. NOUN bjmsr-311 561 2 if if SCONJ bjmsr-311 561 3 jj jj PROPN bjmsr-311 561 4 = = PROPN bjmsr-311 561 5 m2 m2 PROPN bjmsr-311 561 6 go go VERB bjmsr-311 561 7 to to PART bjmsr-311 561 8 step step VERB bjmsr-311 561 9 6.d 6.d NUM bjmsr-311 561 10 ; ; PUNCT bjmsr-311 561 11 otherwise otherwise ADV bjmsr-311 561 12 go go VERB bjmsr-311 561 13 to to PART bjmsr-311 561 14 step step VERB bjmsr-311 561 15 6.a 6.a NUM bjmsr-311 561 16 . . PUNCT bjmsr-311 562 1 d. d. PROPN bjmsr-311 562 2 do do AUX bjmsr-311 562 3 loop loop VERB bjmsr-311 562 4 for for ADP bjmsr-311 562 5 i=1,m2 i=1,m2 NOUN bjmsr-311 562 6 : : PUNCT bjmsr-311 562 7 k k X bjmsr-311 562 8 = = NOUN bjmsr-311 562 9 m m NOUN bjmsr-311 562 10 - - PUNCT bjmsr-311 562 11 i i PROPN bjmsr-311 562 12 , , PUNCT bjmsr-311 562 13 s s PROPN bjmsr-311 562 14 = = NOUN bjmsr-311 562 15 ysol(k ysol(k NOUN bjmsr-311 562 16 ) ) PUNCT bjmsr-311 562 17 ; ; PUNCT bjmsr-311 562 18 do do AUX bjmsr-311 562 19 loop loop VERB bjmsr-311 562 20 for for ADP bjmsr-311 562 21 j j PROPN bjmsr-311 562 22 = = PROPN bjmsr-311 562 23 k k PROPN bjmsr-311 562 24 , , PUNCT bjmsr-311 562 25 m1 m1 PROPN bjmsr-311 562 26 , , PUNCT bjmsr-311 562 27 s s PROPN bjmsr-311 562 28 = = SYM bjmsr-311 562 29 s s NOUN bjmsr-311 562 30 - - PUNCT bjmsr-311 562 31 b(j+1)*xsol(k b(j+1)*xsol(k ADJ bjmsr-311 562 32 , , PUNCT bjmsr-311 562 33 j j NOUN bjmsr-311 562 34 ) ) PUNCT bjmsr-311 562 35 end end NOUN bjmsr-311 562 36 do do VERB bjmsr-311 562 37 , , PUNCT bjmsr-311 562 38 b(k)=s b(k)=s ADV bjmsr-311 562 39 , , PUNCT bjmsr-311 562 40 end end NOUN bjmsr-311 562 41 do do AUX bjmsr-311 562 42 . . PUNCT bjmsr-311 563 1 set set VERB bjmsr-311 563 2 : : PUNCT bjmsr-311 563 3 s s PROPN bjmsr-311 563 4 = = PROPN bjmsr-311 563 5 y(kk(1 y(kk(1 NOUN bjmsr-311 563 6 ) ) PUNCT bjmsr-311 563 7 ) ) PUNCT bjmsr-311 563 8 . . PUNCT bjmsr-311 564 1 do do AUX bjmsr-311 564 2 loop loop VERB bjmsr-311 564 3 for for ADP bjmsr-311 564 4 j=1,m1 j=1,m1 PROPN bjmsr-311 564 5 : : PUNCT bjmsr-311 564 6 s s X bjmsr-311 564 7 = = SYM bjmsr-311 564 8 s s X bjmsr-311 564 9 - - PUNCT bjmsr-311 564 10 b(j+1)*x(kk(1),j b(j+1)*x(kk(1),j NOUN bjmsr-311 564 11 ) ) PUNCT bjmsr-311 564 12 , , PUNCT bjmsr-311 564 13 b(1)=s b(1)= NOUN bjmsr-311 564 14 , , PUNCT bjmsr-311 564 15 end end NOUN bjmsr-311 564 16 do do AUX bjmsr-311 564 17 . . PUNCT bjmsr-311 565 1 print print NOUN bjmsr-311 565 2 : : PUNCT bjmsr-311 565 3 ( ( PUNCT bjmsr-311 565 4 ( ( PUNCT bjmsr-311 565 5 b(j),j=1,m),(kk(j),j=1,m1),lm b(j),j=1,m),(kk(j),j=1,m1),lm NOUN bjmsr-311 565 6 , , PUNCT bjmsr-311 565 7 iter iter NOUN bjmsr-311 565 8 ) ) PUNCT bjmsr-311 565 9 . . PUNCT bjmsr-311 566 1 stop stop VERB bjmsr-311 566 2 . . PUNCT bjmsr-311 567 1 end end VERB bjmsr-311 567 2 the the DET bjmsr-311 567 3 major major ADJ bjmsr-311 567 4 portion portion NOUN bjmsr-311 567 5 of of ADP bjmsr-311 567 6 computation computation NOUN bjmsr-311 567 7 in in ADP bjmsr-311 567 8 this this DET bjmsr-311 567 9 program program NOUN bjmsr-311 567 10 is be AUX bjmsr-311 567 11 the the DET bjmsr-311 567 12 transformation transformation NOUN bjmsr-311 567 13 of of ADP bjmsr-311 567 14 two two NUM bjmsr-311 567 15 - - PUNCT bjmsr-311 567 16 dimensional dimensional ADJ bjmsr-311 567 17 arrays array NOUN bjmsr-311 567 18 . . PUNCT bjmsr-311 568 1 passing pass VERB bjmsr-311 568 2 columns column NOUN bjmsr-311 568 3 of of ADP bjmsr-311 568 4 these these DET bjmsr-311 568 5 arrays array NOUN bjmsr-311 568 6 to to ADP bjmsr-311 568 7 other other ADJ bjmsr-311 568 8 subroutines subroutine NOUN bjmsr-311 568 9 , , PUNCT bjmsr-311 568 10 which which PRON bjmsr-311 568 11 involve involve VERB bjmsr-311 568 12 only only ADV bjmsr-311 568 13 one one NUM bjmsr-311 568 14 - - PUNCT bjmsr-311 568 15 dimensional dimensional ADJ bjmsr-311 568 16 arrays array NOUN bjmsr-311 568 17 saves save VERB bjmsr-311 568 18 the the DET bjmsr-311 568 19 time time NOUN bjmsr-311 568 20 of of ADP bjmsr-311 568 21 computation computation NOUN bjmsr-311 568 22 ( ( PUNCT bjmsr-311 568 23 see see VERB bjmsr-311 568 24 , , PUNCT bjmsr-311 568 25 barrodale barrodale NOUN bjmsr-311 568 26 and and CCONJ bjmsr-311 568 27 roberts roberts PROPN bjmsr-311 568 28 ( ( PUNCT bjmsr-311 568 29 1974 1974 NUM bjmsr-311 568 30 ) ) PUNCT bjmsr-311 568 31 ) ) PUNCT bjmsr-311 568 32 . . PUNCT bjmsr-311 569 1 subroutine subroutine ADJ bjmsr-311 569 2 col1 col1 PROPN bjmsr-311 569 3 , , PUNCT bjmsr-311 569 4 col2 col2 PROPN bjmsr-311 569 5 , , PUNCT bjmsr-311 569 6 and and CCONJ bjmsr-311 569 7 col3 col3 NOUN bjmsr-311 569 8 have have AUX bjmsr-311 569 9 been be AUX bjmsr-311 569 10 coded code VERB bjmsr-311 569 11 to to PART bjmsr-311 569 12 do do VERB bjmsr-311 569 13 this this DET bjmsr-311 569 14 task task NOUN bjmsr-311 569 15 for for ADP bjmsr-311 569 16 subtraction subtraction NOUN bjmsr-311 569 17 , , PUNCT bjmsr-311 569 18 multiplication multiplication NOUN bjmsr-311 569 19 and and CCONJ bjmsr-311 569 20 division division NOUN bjmsr-311 569 21 , , PUNCT bjmsr-311 569 22 and and CCONJ bjmsr-311 569 23 for for ADP bjmsr-311 569 24 only only ADJ bjmsr-311 569 25 division division NOUN bjmsr-311 569 26 respectively respectively ADV bjmsr-311 569 27 . . PUNCT bjmsr-311 570 1 function function NOUN bjmsr-311 570 2 lwmed lwme VERB bjmsr-311 570 3 , , PUNCT bjmsr-311 570 4 which which PRON bjmsr-311 570 5 is be AUX bjmsr-311 570 6 used use VERB bjmsr-311 570 7 to to PART bjmsr-311 570 8 compute compute VERB bjmsr-311 570 9 the the DET bjmsr-311 570 10 weighted weighted ADJ bjmsr-311 570 11 median median NOUN bjmsr-311 570 12 , , PUNCT bjmsr-311 570 13 has have AUX bjmsr-311 570 14 been be AUX bjmsr-311 570 15 introduced introduce VERB bjmsr-311 570 16 in in ADP bjmsr-311 570 17 section section NOUN bjmsr-311 570 18 2.1 2.1 NUM bjmsr-311 570 19 . . PUNCT bjmsr-311 571 1 subroutine subroutine ADJ bjmsr-311 571 2 col1(v1,v2 col1(v1,v2 NOUN bjmsr-311 571 3 ) ) PUNCT bjmsr-311 571 4 step step NOUN bjmsr-311 571 5 0 0 NUM bjmsr-311 571 6 ) ) PUNCT bjmsr-311 571 7 initialization initialization NOUN bjmsr-311 571 8 real real ADJ bjmsr-311 571 9 : : PUNCT bjmsr-311 571 10 v2(1 v2(1 NOUN bjmsr-311 571 11 ) ) PUNCT bjmsr-311 571 12 . . PUNCT bjmsr-311 572 1 common common ADJ bjmsr-311 572 2 /c1 /c1 PROPN bjmsr-311 572 3 / / SYM bjmsr-311 572 4 i1,i2 i1,i2 PROPN bjmsr-311 572 5 . . PUNCT bjmsr-311 573 1 step step NOUN bjmsr-311 573 2 1 1 NUM bjmsr-311 573 3 ) ) PUNCT bjmsr-311 573 4 subtraction subtraction NOUN bjmsr-311 573 5 . . PUNCT bjmsr-311 574 1 copyright copyright NOUN bjmsr-311 574 2 © © PROPN bjmsr-311 574 3 cc cc PROPN bjmsr-311 574 4 - - PUNCT bjmsr-311 574 5 by by ADP bjmsr-311 574 6 - - PUNCT bjmsr-311 574 7 nc nc PROPN bjmsr-311 574 8 2019 2019 NUM bjmsr-311 574 9 , , PUNCT bjmsr-311 574 10 bjmsr bjmsr PROPN bjmsr-311 574 11 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 575 1 bangladesh bangladesh PROPN bjmsr-311 575 2 journal journal PROPN bjmsr-311 575 3 of of ADP bjmsr-311 575 4 multidisciplinary multidisciplinary ADJ bjmsr-311 575 5 scientific scientific ADJ bjmsr-311 575 6 research research NOUN bjmsr-311 575 7 vol vol NOUN bjmsr-311 575 8 . . PROPN bjmsr-311 575 9 1 1 NUM bjmsr-311 575 10 , , PUNCT bjmsr-311 575 11 no no INTJ bjmsr-311 575 12 . . NOUN bjmsr-311 575 13 1 1 NUM bjmsr-311 575 14 ; ; PUNCT bjmsr-311 575 15 2019 2019 NUM bjmsr-311 575 16 17 17 NUM bjmsr-311 575 17 do do AUX bjmsr-311 575 18 loop loop NOUN bjmsr-311 575 19 for for ADP bjmsr-311 575 20 i i PROPN bjmsr-311 575 21 = = PROPN bjmsr-311 575 22 i1,i2 i1,i2 PROPN bjmsr-311 575 23 : : PUNCT bjmsr-311 575 24 v2(i)=v2(i)-v1 v2(i)=v2(i)-v1 PROPN bjmsr-311 575 25 , , PUNCT bjmsr-311 575 26 end end NOUN bjmsr-311 575 27 do do AUX bjmsr-311 575 28 . . PUNCT bjmsr-311 576 1 return return VERB bjmsr-311 576 2 . . PUNCT bjmsr-311 577 1 end end VERB bjmsr-311 577 2 subroutine subroutine NOUN bjmsr-311 577 3 col2(ysk col2(ysk ADJ bjmsr-311 577 4 , , PUNCT bjmsr-311 577 5 jj jj PROPN bjmsr-311 577 6 , , PUNCT bjmsr-311 577 7 v1,ys v1,ys PROPN bjmsr-311 577 8 , , PUNCT bjmsr-311 577 9 v2 v2 PROPN bjmsr-311 577 10 ) ) PUNCT bjmsr-311 577 11 step step NOUN bjmsr-311 577 12 0 0 NUM bjmsr-311 577 13 ) ) PUNCT bjmsr-311 577 14 initialization initialization NOUN bjmsr-311 577 15 . . PUNCT bjmsr-311 578 1 real real ADJ bjmsr-311 578 2 : : PUNCT bjmsr-311 578 3 v1(1),v2(1),ys(1 v1(1),v2(1),ys(1 NOUN bjmsr-311 578 4 ) ) PUNCT bjmsr-311 578 5 . . PUNCT bjmsr-311 579 1 common common ADJ bjmsr-311 579 2 /c1 /c1 PROPN bjmsr-311 579 3 / / SYM bjmsr-311 579 4 i1,i2 i1,i2 PROPN bjmsr-311 579 5 . . PUNCT bjmsr-311 580 1 step step NOUN bjmsr-311 580 2 1 1 NUM bjmsr-311 580 3 ) ) PUNCT bjmsr-311 580 4 compute compute NOUN bjmsr-311 580 5 weights weight NOUN bjmsr-311 580 6 and and CCONJ bjmsr-311 580 7 ratios ratio NOUN bjmsr-311 580 8 . . PUNCT bjmsr-311 581 1 if if SCONJ bjmsr-311 581 2 jj≠1 jj≠1 PROPN bjmsr-311 581 3 go go VERB bjmsr-311 581 4 to to PART bjmsr-311 581 5 step step VERB bjmsr-311 581 6 1.a 1.a NUM bjmsr-311 581 7 , , PUNCT bjmsr-311 581 8 ; ; PUNCT bjmsr-311 581 9 otherwise otherwise ADV bjmsr-311 581 10 do do AUX bjmsr-311 581 11 loop loop VERB bjmsr-311 581 12 for for ADP bjmsr-311 581 13 i i PROPN bjmsr-311 581 14 = = PROPN bjmsr-311 581 15 i1,i2 i1,i2 PROPN bjmsr-311 581 16 : : PUNCT bjmsr-311 581 17 v1(i)=v2(i v1(i)=v2(i NOUN bjmsr-311 581 18 ) ) PUNCT bjmsr-311 581 19 , , PUNCT bjmsr-311 581 20 ys(i)=(ys(i)-ysk)/v2(i ys(i)=(ys(i)-ysk)/v2(i PROPN bjmsr-311 581 21 ) ) PUNCT bjmsr-311 581 22 . . PUNCT bjmsr-311 582 1 return return NOUN bjmsr-311 582 2 . . PUNCT bjmsr-311 583 1 a. a. NOUN bjmsr-311 583 2 do do AUX bjmsr-311 583 3 loop loop VERB bjmsr-311 583 4 for for ADP bjmsr-311 583 5 i i PROPN bjmsr-311 583 6 = = PROPN bjmsr-311 583 7 i1,i2 i1,i2 PROPN bjmsr-311 583 8 : : PUNCT bjmsr-311 583 9 v1(i)=v1(i)*v2(i v1(i)=v1(i)*v2(i ADJ bjmsr-311 583 10 ) ) PUNCT bjmsr-311 583 11 , , PUNCT bjmsr-311 583 12 ys(i)=(ys(i)-ysk)/v2(i ys(i)=(ys(i)-ysk)/v2(i PROPN bjmsr-311 583 13 ) ) PUNCT bjmsr-311 583 14 , , PUNCT bjmsr-311 583 15 end end NOUN bjmsr-311 583 16 do do AUX bjmsr-311 583 17 . . PUNCT bjmsr-311 584 1 return return VERB bjmsr-311 584 2 . . PUNCT bjmsr-311 585 1 end end VERB bjmsr-311 585 2 subroutine subroutine ADJ bjmsr-311 585 3 col3(v1,v2 col3(v1,v2 NOUN bjmsr-311 585 4 ) ) PUNCT bjmsr-311 585 5 step step NOUN bjmsr-311 585 6 0 0 NUM bjmsr-311 585 7 ) ) PUNCT bjmsr-311 585 8 initialization initialization NOUN bjmsr-311 585 9 . . PUNCT bjmsr-311 586 1 real real ADJ bjmsr-311 586 2 : : PUNCT bjmsr-311 586 3 v1(1),v2(1),ys(1 v1(1),v2(1),ys(1 NOUN bjmsr-311 586 4 ) ) PUNCT bjmsr-311 586 5 . . PUNCT bjmsr-311 587 1 common common ADJ bjmsr-311 587 2 /c1 /c1 PROPN bjmsr-311 587 3 / / SYM bjmsr-311 587 4 i1,i2 i1,i2 PROPN bjmsr-311 587 5 . . PUNCT bjmsr-311 588 1 step step NOUN bjmsr-311 588 2 1 1 NUM bjmsr-311 588 3 ) ) PUNCT bjmsr-311 588 4 division division NOUN bjmsr-311 588 5 . . PUNCT bjmsr-311 589 1 do do AUX bjmsr-311 589 2 loop loop VERB bjmsr-311 589 3 for for ADP bjmsr-311 589 4 i i PROPN bjmsr-311 589 5 = = PROPN bjmsr-311 589 6 i1,i2 i1,i2 PROPN bjmsr-311 589 7 : : PUNCT bjmsr-311 589 8 v1(i)=v1(i)/v2(i v1(i)=v1(i)/v2(i NOUN bjmsr-311 589 9 ) ) PUNCT bjmsr-311 589 10 , , PUNCT bjmsr-311 589 11 end end NOUN bjmsr-311 589 12 do do AUX bjmsr-311 589 13 . . PUNCT bjmsr-311 590 1 return return VERB bjmsr-311 590 2 . . PUNCT bjmsr-311 591 1 end end VERB bjmsr-311 591 2 4.4 4.4 NUM bjmsr-311 591 3 initial initial ADJ bjmsr-311 591 4 value value NOUN bjmsr-311 591 5 problem problem NOUN bjmsr-311 591 6 selection selection NOUN bjmsr-311 591 7 of of ADP bjmsr-311 591 8 the the DET bjmsr-311 591 9 arbitrary arbitrary ADJ bjmsr-311 591 10 points point NOUN bjmsr-311 591 11 k1,k2, k1,k2, NOUN bjmsr-311 591 12 ... ... PUNCT bjmsr-311 591 13 ,k(m-1 ,k(m-1 PUNCT bjmsr-311 591 14 ) ) PUNCT bjmsr-311 591 15 at at ADP bjmsr-311 591 16 the the DET bjmsr-311 591 17 first first ADJ bjmsr-311 591 18 stage stage NOUN bjmsr-311 591 19 of of ADP bjmsr-311 591 20 computation computation NOUN bjmsr-311 591 21 has have VERB bjmsr-311 591 22 an an DET bjmsr-311 591 23 important important ADJ bjmsr-311 591 24 role role NOUN bjmsr-311 591 25 in in ADP bjmsr-311 591 26 the the DET bjmsr-311 591 27 number number NOUN bjmsr-311 591 28 of of ADP bjmsr-311 591 29 iterations iteration NOUN bjmsr-311 591 30 necessary necessary ADJ bjmsr-311 591 31 to to PART bjmsr-311 591 32 reach reach VERB bjmsr-311 591 33 the the DET bjmsr-311 591 34 optimal optimal ADJ bjmsr-311 591 35 solution solution NOUN bjmsr-311 591 36 . . PUNCT bjmsr-311 592 1 one one NUM bjmsr-311 592 2 way way NOUN bjmsr-311 592 3 to to PART bjmsr-311 592 4 select select VERB bjmsr-311 592 5 these these DET bjmsr-311 592 6 m-1 m-1 NUM bjmsr-311 592 7 points point NOUN bjmsr-311 592 8 may may AUX bjmsr-311 592 9 be be AUX bjmsr-311 592 10 based base VERB bjmsr-311 592 11 on on ADP bjmsr-311 592 12 applying apply VERB bjmsr-311 592 13 another another DET bjmsr-311 592 14 estimator estimator NOUN bjmsr-311 592 15 to to PART bjmsr-311 592 16 guess guess VERB bjmsr-311 592 17 those those DET bjmsr-311 592 18 points point NOUN bjmsr-311 592 19 which which PRON bjmsr-311 592 20 their their PRON bjmsr-311 592 21 residuals residual NOUN bjmsr-311 592 22 are be AUX bjmsr-311 592 23 smallest small ADJ bjmsr-311 592 24 in in ADP bjmsr-311 592 25 absolute absolute ADJ bjmsr-311 592 26 values value NOUN bjmsr-311 592 27 among among ADP bjmsr-311 592 28 all all DET bjmsr-311 592 29 estimated estimate VERB bjmsr-311 592 30 residuals residual NOUN bjmsr-311 592 31 . . PUNCT bjmsr-311 593 1 that that PRON bjmsr-311 593 2 is be AUX bjmsr-311 593 3 one one NUM bjmsr-311 593 4 estimator estimator NOUN bjmsr-311 593 5 for for ADP bjmsr-311 593 6 example example NOUN bjmsr-311 593 7 least least ADJ bjmsr-311 593 8 squares square NOUN bjmsr-311 593 9 is be AUX bjmsr-311 593 10 applied apply VERB bjmsr-311 593 11 on on ADP bjmsr-311 593 12 the the DET bjmsr-311 593 13 data datum NOUN bjmsr-311 593 14 , , PUNCT bjmsr-311 593 15 and and CCONJ bjmsr-311 593 16 smallest small ADJ bjmsr-311 593 17 m-1 m-1 NOUN bjmsr-311 593 18 residuals residual NOUN bjmsr-311 593 19 in in ADP bjmsr-311 593 20 absolute absolute ADJ bjmsr-311 593 21 values value NOUN bjmsr-311 593 22 are be AUX bjmsr-311 593 23 selected select VERB bjmsr-311 593 24 , , PUNCT bjmsr-311 593 25 and and CCONJ bjmsr-311 593 26 the the DET bjmsr-311 593 27 corresponding corresponding ADJ bjmsr-311 593 28 points point NOUN bjmsr-311 593 29 to to ADP bjmsr-311 593 30 these these DET bjmsr-311 593 31 residuals residual NOUN bjmsr-311 593 32 are be AUX bjmsr-311 593 33 nominated nominate VERB bjmsr-311 593 34 for for ADP bjmsr-311 593 35 starting start VERB bjmsr-311 593 36 algorithms algorithm NOUN bjmsr-311 593 37 1 1 NUM bjmsr-311 593 38 , , PUNCT bjmsr-311 593 39 2 2 NUM bjmsr-311 593 40 , , PUNCT bjmsr-311 593 41 3 3 NUM bjmsr-311 593 42 or or CCONJ bjmsr-311 593 43 4 4 NUM bjmsr-311 593 44 . . PUNCT bjmsr-311 594 1 however however ADV bjmsr-311 594 2 , , PUNCT bjmsr-311 594 3 we we PRON bjmsr-311 594 4 examined examine VERB bjmsr-311 594 5 this this DET bjmsr-311 594 6 procedure procedure NOUN bjmsr-311 594 7 for for ADP bjmsr-311 594 8 algorithms algorithm NOUN bjmsr-311 594 9 2 2 NUM bjmsr-311 594 10 and and CCONJ bjmsr-311 594 11 4 4 NUM bjmsr-311 594 12 and and CCONJ bjmsr-311 594 13 found find VERB bjmsr-311 594 14 that that SCONJ bjmsr-311 594 15 it it PRON bjmsr-311 594 16 makes make VERB bjmsr-311 594 17 them they PRON bjmsr-311 594 18 more more ADV bjmsr-311 594 19 efficient efficient ADJ bjmsr-311 594 20 . . PUNCT bjmsr-311 595 1 in in ADP bjmsr-311 595 2 the the DET bjmsr-311 595 3 process process NOUN bjmsr-311 595 4 of of ADP bjmsr-311 595 5 this this DET bjmsr-311 595 6 study study NOUN bjmsr-311 595 7 , , PUNCT bjmsr-311 595 8 we we PRON bjmsr-311 595 9 found find VERB bjmsr-311 595 10 some some DET bjmsr-311 595 11 points point NOUN bjmsr-311 595 12 which which PRON bjmsr-311 595 13 might might AUX bjmsr-311 595 14 be be AUX bjmsr-311 595 15 leading lead VERB bjmsr-311 595 16 to to PART bjmsr-311 595 17 develop develop VERB bjmsr-311 595 18 the the DET bjmsr-311 595 19 field field NOUN bjmsr-311 595 20 of of ADP bjmsr-311 595 21 l1 l1 PROPN bjmsr-311 595 22 norm norm NOUN bjmsr-311 595 23 computation computation NOUN bjmsr-311 595 24 . . PUNCT bjmsr-311 596 1 in in ADP bjmsr-311 596 2 the the DET bjmsr-311 596 3 proposed propose VERB bjmsr-311 596 4 algorithm algorithm NOUN bjmsr-311 596 5 4 4 NUM bjmsr-311 596 6 , , PUNCT bjmsr-311 596 7 we we PRON bjmsr-311 596 8 could could AUX bjmsr-311 596 9 not not PART bjmsr-311 596 10 find find VERB bjmsr-311 596 11 a a DET bjmsr-311 596 12 criterion criterion NOUN bjmsr-311 596 13 to to PART bjmsr-311 596 14 delete delete VERB bjmsr-311 596 15 that that DET bjmsr-311 596 16 observation observation NOUN bjmsr-311 596 17 from from ADP bjmsr-311 596 18 the the DET bjmsr-311 596 19 current current ADJ bjmsr-311 596 20 set set NOUN bjmsr-311 596 21 of of ADP bjmsr-311 596 22 observations observation NOUN bjmsr-311 596 23 on on ADP bjmsr-311 596 24 the the DET bjmsr-311 596 25 basis basis NOUN bjmsr-311 596 26 , , PUNCT bjmsr-311 596 27 which which PRON bjmsr-311 596 28 reduces reduce VERB bjmsr-311 596 29 the the DET bjmsr-311 596 30 objective objective ADJ bjmsr-311 596 31 function function NOUN bjmsr-311 596 32 value value NOUN bjmsr-311 596 33 more more ADJ bjmsr-311 596 34 than than ADP bjmsr-311 596 35 other other ADJ bjmsr-311 596 36 points point NOUN bjmsr-311 596 37 . . PUNCT bjmsr-311 597 1 if if SCONJ bjmsr-311 597 2 anyone anyone PRON bjmsr-311 597 3 finds find VERB bjmsr-311 597 4 a a DET bjmsr-311 597 5 criterion criterion NOUN bjmsr-311 597 6 like like ADP bjmsr-311 597 7 the the DET bjmsr-311 597 8 heuristic heuristic ADJ bjmsr-311 597 9 method method NOUN bjmsr-311 597 10 of of ADP bjmsr-311 597 11 bloomfield bloomfield PROPN bjmsr-311 597 12 and and CCONJ bjmsr-311 597 13 steiger steiger PROPN bjmsr-311 597 14 ( ( PUNCT bjmsr-311 597 15 1980 1980 NUM bjmsr-311 597 16 ) ) PUNCT bjmsr-311 597 17 , , PUNCT bjmsr-311 597 18 the the DET bjmsr-311 597 19 number number NOUN bjmsr-311 597 20 of of ADP bjmsr-311 597 21 iterations iteration NOUN bjmsr-311 597 22 will will AUX bjmsr-311 597 23 decrease decrease VERB bjmsr-311 597 24 very very ADV bjmsr-311 597 25 much much ADV bjmsr-311 597 26 and and CCONJ bjmsr-311 597 27 will will AUX bjmsr-311 597 28 reduce reduce VERB bjmsr-311 597 29 computation computation NOUN bjmsr-311 597 30 time time NOUN bjmsr-311 597 31 . . PUNCT bjmsr-311 598 1 the the DET bjmsr-311 598 2 main main ADJ bjmsr-311 598 3 obstacle obstacle NOUN bjmsr-311 598 4 to to ADP bjmsr-311 598 5 applying apply VERB bjmsr-311 598 6 discrete discrete ADJ bjmsr-311 598 7 differentiation differentiation NOUN bjmsr-311 598 8 technique technique NOUN bjmsr-311 598 9 to to ADP bjmsr-311 598 10 operational operational ADJ bjmsr-311 598 11 problems problem NOUN bjmsr-311 598 12 is be AUX bjmsr-311 598 13 reordering reorder VERB bjmsr-311 598 14 of of ADP bjmsr-311 598 15 the the DET bjmsr-311 598 16 residuals residual NOUN bjmsr-311 598 17 in in ADP bjmsr-311 598 18 descending descend VERB bjmsr-311 598 19 order order NOUN bjmsr-311 598 20 before before ADP bjmsr-311 598 21 starting start VERB bjmsr-311 598 22 the the DET bjmsr-311 598 23 computation computation NOUN bjmsr-311 598 24 . . PUNCT bjmsr-311 599 1 if if SCONJ bjmsr-311 599 2 this this DET bjmsr-311 599 3 obstacle obstacle NOUN bjmsr-311 599 4 is be AUX bjmsr-311 599 5 removed remove VERB bjmsr-311 599 6 , , PUNCT bjmsr-311 599 7 a a DET bjmsr-311 599 8 similar similar ADJ bjmsr-311 599 9 algorithm algorithm NOUN bjmsr-311 599 10 to to ADP bjmsr-311 599 11 that that PRON bjmsr-311 599 12 of of ADP bjmsr-311 599 13 simple simple ADJ bjmsr-311 599 14 restricted restrict VERB bjmsr-311 599 15 linear linear ADJ bjmsr-311 599 16 regression regression NOUN bjmsr-311 599 17 for for ADP bjmsr-311 599 18 multiple multiple ADJ bjmsr-311 599 19 regression regression NOUN bjmsr-311 599 20 may may AUX bjmsr-311 599 21 be be AUX bjmsr-311 599 22 proposed propose VERB bjmsr-311 599 23 . . PUNCT bjmsr-311 600 1 references reference NOUN bjmsr-311 600 2 i. i. PROPN bjmsr-311 600 3 barrodale barrodale PROPN bjmsr-311 600 4 , , PUNCT bjmsr-311 600 5 f.d.k f.d.k NOUN bjmsr-311 600 6 . . PUNCT bjmsr-311 601 1 roberts roberts PROPN bjmsr-311 601 2 ( ( PUNCT bjmsr-311 601 3 1974 1974 NUM bjmsr-311 601 4 ) ) PUNCT bjmsr-311 601 5 algorithm algorithm NOUN bjmsr-311 601 6 478 478 NUM bjmsr-311 601 7 : : PUNCT bjmsr-311 601 8 solution solution NOUN bjmsr-311 601 9 of of ADP bjmsr-311 601 10 an an DET bjmsr-311 601 11 overdetermined overdetermine VERB bjmsr-311 601 12 system system NOUN bjmsr-311 601 13 of of ADP bjmsr-311 601 14 equations equation NOUN bjmsr-311 601 15 in in ADP bjmsr-311 601 16 the the DET bjmsr-311 601 17 l l NOUN bjmsr-311 601 18 1 1 NUM bjmsr-311 601 19 norm norm NOUN bjmsr-311 601 20 . . PUNCT bjmsr-311 602 1 comm comm NOUN bjmsr-311 602 2 . . PUNCT bjmsr-311 602 3 acm acm PROPN bjmsr-311 602 4 , , PUNCT bjmsr-311 602 5 17 17 NUM bjmsr-311 602 6 , , PUNCT bjmsr-311 602 7 319 319 NUM bjmsr-311 602 8 - - SYM bjmsr-311 602 9 320 320 NUM bjmsr-311 602 10 . . PUNCT bjmsr-311 603 1 c.m c.m PROPN bjmsr-311 603 2 . . PROPN bjmsr-311 603 3 bender bender PROPN bjmsr-311 603 4 , , PUNCT bjmsr-311 603 5 s.a s.a PROPN bjmsr-311 603 6 . . PROPN bjmsr-311 603 7 orszag orszag PROPN bjmsr-311 603 8 ( ( PUNCT bjmsr-311 603 9 1978 1978 NUM bjmsr-311 603 10 ) ) PUNCT bjmsr-311 603 11 advanced advanced ADJ bjmsr-311 603 12 mathematical mathematical ADJ bjmsr-311 603 13 methods method NOUN bjmsr-311 603 14 for for ADP bjmsr-311 603 15 scientists scientist NOUN bjmsr-311 603 16 and and CCONJ bjmsr-311 603 17 engineers engineer NOUN bjmsr-311 603 18 , , PUNCT bjmsr-311 603 19 mcgraw mcgraw PROPN bjmsr-311 603 20 - - PUNCT bjmsr-311 603 21 hill hill NOUN bjmsr-311 603 22 . . PUNCT bjmsr-311 604 1 bijan bijan PROPN bjmsr-311 604 2 bidabad bidabad NOUN bjmsr-311 604 3 ( ( PUNCT bjmsr-311 604 4 1987a 1987a NUM bjmsr-311 604 5 ) ) PUNCT bjmsr-311 604 6 least least ADJ bjmsr-311 604 7 absolute absolute ADJ bjmsr-311 604 8 error error NOUN bjmsr-311 604 9 estimation estimation NOUN bjmsr-311 604 10 . . PUNCT bjmsr-311 605 1 the the DET bjmsr-311 605 2 first first ADJ bjmsr-311 605 3 international international ADJ bjmsr-311 605 4 conference conference NOUN bjmsr-311 605 5 on on ADP bjmsr-311 605 6 statistical statistical ADJ bjmsr-311 605 7 data datum NOUN bjmsr-311 605 8 analysis analysis NOUN bjmsr-311 605 9 based base VERB bjmsr-311 605 10 on on ADP bjmsr-311 605 11 the the DET bjmsr-311 605 12 l1‎‎ l1‎‎ ADJ bjmsr-311 605 13 norm norm NOUN bjmsr-311 605 14 and and CCONJ bjmsr-311 605 15 related related ADJ bjmsr-311 605 16 methods method NOUN bjmsr-311 605 17 , , PUNCT bjmsr-311 605 18 neuchatel neuchatel NOUN bjmsr-311 605 19 , , PUNCT bjmsr-311 605 20 switzerland switzerland PROPN bjmsr-311 605 21 . . PUNCT bjmsr-311 606 1 http://www.bidabad.com/doc/lae-i.pdf http://www.bidabad.com/doc/lae-i.pdf PROPN bjmsr-311 606 2 bijan bijan PROPN bjmsr-311 606 3 bidabad bidabad NOUN bjmsr-311 606 4 ( ( PUNCT bjmsr-311 606 5 1987b 1987b NUM bjmsr-311 606 6 ) ) PUNCT bjmsr-311 606 7 least least ADJ bjmsr-311 606 8 absolute absolute ADJ bjmsr-311 606 9 error error NOUN bjmsr-311 606 10 estimation estimation NOUN bjmsr-311 606 11 , , PUNCT bjmsr-311 606 12 part part PROPN bjmsr-311 606 13 ii ii PROPN bjmsr-311 606 14 . . PROPN bjmsr-311 606 15 submitted submit VERB bjmsr-311 606 16 to to ADP bjmsr-311 606 17 the the DET bjmsr-311 606 18 first first ADJ bjmsr-311 606 19 international international ADJ bjmsr-311 606 20 conference conference NOUN bjmsr-311 606 21 on on ADP bjmsr-311 606 22 statistical statistical ADJ bjmsr-311 606 23 data datum NOUN bjmsr-311 606 24 analysis analysis NOUN bjmsr-311 606 25 based base VERB bjmsr-311 606 26 on on ADP bjmsr-311 606 27 the the DET bjmsr-311 606 28 l1‎‎ l1‎‎ ADJ bjmsr-311 606 29 norm norm NOUN bjmsr-311 606 30 and and CCONJ bjmsr-311 606 31 related related ADJ bjmsr-311 606 32 methods method NOUN bjmsr-311 606 33 , , PUNCT bjmsr-311 606 34 neuchatel neuchatel NOUN bjmsr-311 606 35 , , PUNCT bjmsr-311 606 36 switzerland switzerland PROPN bjmsr-311 606 37 . . PUNCT bjmsr-311 607 1 http://www.bidabad.com/doc/lae-ii.pdf http://www.bidabad.com/doc/lae-ii.pdf PROPN bjmsr-311 607 2 bijan bijan PROPN bjmsr-311 607 3 bidabad bidabad NOUN bjmsr-311 607 4 ( ( PUNCT bjmsr-311 607 5 1988a 1988a NUM bjmsr-311 607 6 ) ) PUNCT bjmsr-311 607 7 a a DET bjmsr-311 607 8 proposed propose VERB bjmsr-311 607 9 algorithm algorithm NOUN bjmsr-311 607 10 for for ADP bjmsr-311 607 11 least least ADJ bjmsr-311 607 12 absolute absolute ADJ bjmsr-311 607 13 error error NOUN bjmsr-311 607 14 estimation estimation NOUN bjmsr-311 607 15 . . PUNCT bjmsr-311 608 1 proc proc PROPN bjmsr-311 608 2 . . PUNCT bjmsr-311 609 1 of of ADP bjmsr-311 609 2 the the DET bjmsr-311 609 3 third third ADJ bjmsr-311 609 4 seminar seminar NOUN bjmsr-311 609 5 of of ADP bjmsr-311 609 6 mathematical mathematical ADJ bjmsr-311 609 7 analysis analysis NOUN bjmsr-311 609 8 . . PUNCT bjmsr-311 610 1 shiraz shiraz PROPN bjmsr-311 610 2 univ univ PROPN bjmsr-311 610 3 . . PROPN bjmsr-311 610 4 , , PUNCT bjmsr-311 610 5 24 24 NUM bjmsr-311 610 6 - - SYM bjmsr-311 610 7 34 34 NUM bjmsr-311 610 8 , , PUNCT bjmsr-311 610 9 shiraz shiraz PROPN bjmsr-311 610 10 , , PUNCT bjmsr-311 610 11 iran iran PROPN bjmsr-311 610 12 . . PUNCT bjmsr-311 611 1 bijan bijan PROPN bjmsr-311 611 2 bidabad bidabad NOUN bjmsr-311 611 3 ( ( PUNCT bjmsr-311 611 4 1988b 1988b NUM bjmsr-311 611 5 ) ) PUNCT bjmsr-311 611 6 a a DET bjmsr-311 611 7 proposed propose VERB bjmsr-311 611 8 algorithm algorithm NOUN bjmsr-311 611 9 for for ADP bjmsr-311 611 10 least least ADJ bjmsr-311 611 11 absolute absolute ADJ bjmsr-311 611 12 error error NOUN bjmsr-311 611 13 estimation estimation NOUN bjmsr-311 611 14 , , PUNCT bjmsr-311 611 15 part part PROPN bjmsr-311 611 16 ii ii PROPN bjmsr-311 611 17 . . PUNCT bjmsr-311 611 18 proc proc PROPN bjmsr-311 611 19 . . PUNCT bjmsr-311 612 1 of of ADP bjmsr-311 612 2 the the DET bjmsr-311 612 3 third third ADJ bjmsr-311 612 4 seminar seminar NOUN bjmsr-311 612 5 of of ADP bjmsr-311 612 6 mathematical mathematical ADJ bjmsr-311 612 7 analysis analysis NOUN bjmsr-311 612 8 , , PUNCT bjmsr-311 612 9 shiraz shiraz PROPN bjmsr-311 612 10 univ univ PROPN bjmsr-311 612 11 . . PROPN bjmsr-311 612 12 , , PUNCT bjmsr-311 612 13 35 35 NUM bjmsr-311 612 14 - - SYM bjmsr-311 612 15 50 50 NUM bjmsr-311 612 16 , , PUNCT bjmsr-311 612 17 shiraz shiraz NOUN bjmsr-311 612 18 , , PUNCT bjmsr-311 612 19 iran iran PROPN bjmsr-311 612 20 . . PUNCT bjmsr-311 613 1 bijan bijan PROPN bjmsr-311 613 2 bidabad bidabad NOUN bjmsr-311 613 3 ( ( PUNCT bjmsr-311 613 4 1989a 1989a NUM bjmsr-311 613 5 ) ) PUNCT bjmsr-311 613 6 discrete discrete ADJ bjmsr-311 613 7 and and CCONJ bjmsr-311 613 8 continuous continuous ADJ bjmsr-311 613 9 l1‎‎ l1‎‎ ADJ bjmsr-311 613 10 norm norm NOUN bjmsr-311 613 11 regressions regression NOUN bjmsr-311 613 12 , , PUNCT bjmsr-311 613 13 proposition proposition NOUN bjmsr-311 613 14 of of ADP bjmsr-311 613 15 discrete discrete ADJ bjmsr-311 613 16 approximation approximation NOUN bjmsr-311 613 17 algorithms algorithm NOUN bjmsr-311 613 18 and and CCONJ bjmsr-311 613 19 http://www.bidabad.com/doc/lae-i.pdf http://www.bidabad.com/doc/lae-i.pdf PRON bjmsr-311 613 20 http://www.bidabad.com/doc/lae-ii.pdf http://www.bidabad.com/doc/lae-ii.pdf ADJ bjmsr-311 613 21 copyright copyright NOUN bjmsr-311 613 22 © © PROPN bjmsr-311 613 23 cc cc PROPN bjmsr-311 613 24 - - PUNCT bjmsr-311 613 25 by by ADP bjmsr-311 613 26 - - PUNCT bjmsr-311 613 27 nc nc PROPN bjmsr-311 613 28 2019 2019 NUM bjmsr-311 613 29 , , PUNCT bjmsr-311 613 30 bjmsr bjmsr PROPN bjmsr-311 613 31 www.cribfb.com/journal/index.php/bjmsr www.cribfb.com/journal/index.php/bjmsr X bjmsr-311 614 1 bangladesh bangladesh PROPN bjmsr-311 614 2 journal journal PROPN bjmsr-311 614 3 of of ADP bjmsr-311 614 4 multidisciplinary multidisciplinary ADJ bjmsr-311 614 5 scientific scientific ADJ bjmsr-311 614 6 research research NOUN bjmsr-311 614 7 vol vol NOUN bjmsr-311 614 8 . . PROPN bjmsr-311 614 9 1 1 NUM bjmsr-311 614 10 , , PUNCT bjmsr-311 614 11 no no INTJ bjmsr-311 614 12 . . NOUN bjmsr-311 614 13 1 1 NUM bjmsr-311 614 14 ; ; PUNCT bjmsr-311 614 15 2019 2019 NUM bjmsr-311 614 16 18 18 NUM bjmsr-311 614 17 continuous continuous ADJ bjmsr-311 614 18 smoothing smoothing NOUN bjmsr-311 614 19 of of ADP bjmsr-311 614 20 concentration concentration NOUN bjmsr-311 614 21 surface surface NOUN bjmsr-311 614 22 , , PUNCT bjmsr-311 614 23 ph.d ph.d PROPN bjmsr-311 614 24 . . PUNCT bjmsr-311 615 1 thesis thesis PROPN bjmsr-311 615 2 , , PUNCT bjmsr-311 615 3 islamic islamic PROPN bjmsr-311 615 4 azad azad PROPN bjmsr-311 615 5 univ univ PROPN bjmsr-311 615 6 . . PROPN bjmsr-311 615 7 , , PUNCT bjmsr-311 615 8 tehran tehran PROPN bjmsr-311 615 9 , , PUNCT bjmsr-311 615 10 iran iran PROPN bjmsr-311 615 11 . . PUNCT bjmsr-311 616 1 http://www.bidabad.com/doc/l1-norm-thesis-en.pdf http://www.bidabad.com/doc/l1-norm-thesis-en.pdf PROPN bjmsr-311 616 2 bijan bijan PROPN bjmsr-311 616 3 bidabad bidabad NOUN bjmsr-311 616 4 ( ( PUNCT bjmsr-311 616 5 1989b 1989b NUM bjmsr-311 616 6 ) ) PUNCT bjmsr-311 616 7 discrete discrete ADJ bjmsr-311 616 8 and and CCONJ bjmsr-311 616 9 continuous continuous ADJ bjmsr-311 616 10 l1‎‎ l1‎‎ ADJ bjmsr-311 616 11 norm norm NOUN bjmsr-311 616 12 regressions regression NOUN bjmsr-311 616 13 , , PUNCT bjmsr-311 616 14 proposition proposition NOUN bjmsr-311 616 15 of of ADP bjmsr-311 616 16 discrete discrete ADJ bjmsr-311 616 17 approximation approximation NOUN bjmsr-311 616 18 algorithms algorithm NOUN bjmsr-311 616 19 and and CCONJ bjmsr-311 616 20 continuous continuous ADJ bjmsr-311 616 21 smoothing smoothing NOUN bjmsr-311 616 22 of of ADP bjmsr-311 616 23 concentration concentration NOUN bjmsr-311 616 24 surface surface NOUN bjmsr-311 616 25 , , PUNCT bjmsr-311 616 26 ph.d ph.d PROPN bjmsr-311 616 27 . . PUNCT bjmsr-311 617 1 thesis thesis PROPN bjmsr-311 617 2 , , PUNCT bjmsr-311 617 3 islamic islamic PROPN bjmsr-311 617 4 azad azad PROPN bjmsr-311 617 5 univ univ PROPN bjmsr-311 617 6 . . PROPN bjmsr-311 617 7 , , PUNCT bjmsr-311 617 8 tehran tehran PROPN bjmsr-311 617 9 , , PUNCT bjmsr-311 617 10 iran iran PROPN bjmsr-311 617 11 . . PUNCT bjmsr-311 618 1 farsi farsi PROPN bjmsr-311 618 2 translation translation NOUN bjmsr-311 618 3 . . PUNCT bjmsr-311 619 1 http://www.bidabad.com/doc/l1-norm-thesis-fa.pdf http://www.bidabad.com/doc/l1-norm-thesis-fa.pdf PROPN bjmsr-311 619 2 bijan bijan PROPN bjmsr-311 619 3 bidabad bidabad NOUN bjmsr-311 619 4 ( ( PUNCT bjmsr-311 619 5 2005 2005 NUM bjmsr-311 619 6 ) ) PUNCT bjmsr-311 619 7 . . PUNCT bjmsr-311 620 1 l1 l1 PROPN bjmsr-311 620 2 norm norm PROPN bjmsr-311 620 3 based base VERB bjmsr-311 620 4 computational computational ADJ bjmsr-311 620 5 algorithms algorithm NOUN bjmsr-311 620 6 . . PUNCT bjmsr-311 621 1 http://www.bidabad.com/doc/l1-article6.pdf http://www.bidabad.com/doc/l1-article6.pdf PROPN bjmsr-311 621 2 bijan bijan PROPN bjmsr-311 621 3 bidabad bidabad NOUN bjmsr-311 621 4 ( ( PUNCT bjmsr-311 621 5 2005 2005 NUM bjmsr-311 621 6 ) ) PUNCT bjmsr-311 621 7 . . PUNCT bjmsr-311 622 1 l1 l1 PROPN bjmsr-311 622 2 norm norm NOUN bjmsr-311 622 3 solution solution NOUN bjmsr-311 622 4 of of ADP bjmsr-311 622 5 overdetermined overdetermined ADJ bjmsr-311 622 6 system system NOUN bjmsr-311 622 7 of of ADP bjmsr-311 622 8 linear linear PROPN bjmsr-311 622 9 equations equation NOUN bjmsr-311 622 10 . . PUNCT bjmsr-311 623 1 http://www.bidabad.com/doc/l1article5.pdf http://www.bidabad.com/doc/l1article5.pdf PROPN bjmsr-311 623 2 bijan bijan PROPN bjmsr-311 623 3 bidabad bidabad NOUN bjmsr-311 623 4 ( ( PUNCT bjmsr-311 623 5 2005 2005 NUM bjmsr-311 623 6 ) ) PUNCT bjmsr-311 623 7 . . PUNCT bjmsr-311 624 1 l1 l1 PROPN bjmsr-311 624 2 norm norm PROPN bjmsr-311 624 3 based base VERB bjmsr-311 624 4 data datum NOUN bjmsr-311 624 5 analysis analysis NOUN bjmsr-311 624 6 and and CCONJ bjmsr-311 624 7 related related ADJ bjmsr-311 624 8 methods method NOUN bjmsr-311 624 9 . . PUNCT bjmsr-311 625 1 http://www.bidabad.com/doc/l1-articl1.pdf http://www.bidabad.com/doc/l1-articl1.pdf PROPN bjmsr-311 625 2 bijan bijan PROPN bjmsr-311 625 3 bidabad bidabad NOUN bjmsr-311 625 4 ( ( PUNCT bjmsr-311 625 5 2005 2005 NUM bjmsr-311 625 6 ) ) PUNCT bjmsr-311 625 7 . . PUNCT bjmsr-311 626 1 new new ADJ bjmsr-311 626 2 algorithms algorithm NOUN bjmsr-311 626 3 for for ADP bjmsr-311 626 4 the the DET bjmsr-311 626 5 l1 l1 PROPN bjmsr-311 626 6 norm norm NOUN bjmsr-311 626 7 regression regression NOUN bjmsr-311 626 8 . . PUNCT bjmsr-311 627 1 http://www.bidabad.com/doc/l1-article2.pdf http://www.bidabad.com/doc/l1-article2.pdf ADJ bjmsr-311 627 2 bijan bijan NOUN bjmsr-311 627 3 bidabad bidabad NOUN bjmsr-311 627 4 ( ( PUNCT bjmsr-311 627 5 2005 2005 NUM bjmsr-311 627 6 ) ) PUNCT bjmsr-311 627 7 . . PUNCT bjmsr-311 628 1 comparative comparative ADJ bjmsr-311 628 2 study study NOUN bjmsr-311 628 3 of of ADP bjmsr-311 628 4 the the DET bjmsr-311 628 5 l1 l1 PROPN bjmsr-311 628 6 norm norm PROPN bjmsr-311 628 7 regression regression NOUN bjmsr-311 628 8 algorithms algorithm NOUN bjmsr-311 628 9 . . PUNCT bjmsr-311 629 1 http://www.bidabad.com/doc/l1-articl3.pdf http://www.bidabad.com/doc/l1-articl3.pdf PROPN bjmsr-311 629 2 bijan bijan PROPN bjmsr-311 629 3 bidabad bidabad NOUN bjmsr-311 629 4 ( ( PUNCT bjmsr-311 629 5 2005 2005 NUM bjmsr-311 629 6 ) ) PUNCT bjmsr-311 629 7 . . PUNCT bjmsr-311 630 1 continuous continuous ADJ bjmsr-311 630 2 l1 l1 PROPN bjmsr-311 630 3 norm norm NOUN bjmsr-311 630 4 estimation estimation NOUN bjmsr-311 630 5 of of ADP bjmsr-311 630 6 lorenz lorenz PROPN bjmsr-311 630 7 curve curve PROPN bjmsr-311 630 8 . . PUNCT bjmsr-311 631 1 http://www.bidabad.com/doc/l1-articl4.pdf http://www.bidabad.com/doc/l1-articl4.pdf PROPN bjmsr-311 631 2 bijan bijan PROPN bjmsr-311 631 3 bidabad bidabad NOUN bjmsr-311 631 4 ( ( PUNCT bjmsr-311 631 5 1993 1993 NUM bjmsr-311 631 6 ) ) PUNCT bjmsr-311 631 7 . . PUNCT bjmsr-311 632 1 estimating estimate VERB bjmsr-311 632 2 lorenz lorenz PROPN bjmsr-311 632 3 curve curve NOUN bjmsr-311 632 4 for for ADP bjmsr-311 632 5 iran iran PROPN bjmsr-311 632 6 by by ADP bjmsr-311 632 7 using use VERB bjmsr-311 632 8 continuous continuous ADJ bjmsr-311 632 9 l1 l1 PROPN bjmsr-311 632 10 norm norm NOUN bjmsr-311 632 11 estimation estimation PROPN bjmsr-311 632 12 , , PUNCT bjmsr-311 632 13 economics economic NOUN bjmsr-311 632 14 and and CCONJ bjmsr-311 632 15 management management NOUN bjmsr-311 632 16 journal journal NOUN bjmsr-311 632 17 , , PUNCT bjmsr-311 632 18 islamic islamic PROPN bjmsr-311 632 19 azad azad PROPN bjmsr-311 632 20 university university PROPN bjmsr-311 632 21 , , PUNCT bjmsr-311 632 22 no no INTJ bjmsr-311 632 23 . . NOUN bjmsr-311 632 24 19 19 NUM bjmsr-311 632 25 , , PUNCT bjmsr-311 632 26 winter winter NOUN bjmsr-311 632 27 1993 1993 NUM bjmsr-311 632 28 , , PUNCT bjmsr-311 632 29 pp pp ADV bjmsr-311 632 30 . . PUNCT bjmsr-311 633 1 83 83 NUM bjmsr-311 633 2 - - SYM bjmsr-311 633 3 101 101 NUM bjmsr-311 633 4 . . PUNCT bjmsr-311 634 1 http://www.bidabad.com/doc/iraninc-l1.pdf http://www.bidabad.com/doc/iraninc-l1.pdf PROPN bjmsr-311 634 2 bijan bijan PROPN bjmsr-311 634 3 bidabad bidabad NOUN bjmsr-311 634 4 ( ( PUNCT bjmsr-311 634 5 2005 2005 NUM bjmsr-311 634 6 ) ) PUNCT bjmsr-311 634 7 . . PUNCT bjmsr-311 635 1 continuous continuous ADJ bjmsr-311 635 2 l1 l1 PROPN bjmsr-311 635 3 norm norm NOUN bjmsr-311 635 4 estimation estimation NOUN bjmsr-311 635 5 of of ADP bjmsr-311 635 6 lorenz lorenz PROPN bjmsr-311 635 7 curve curve VERB bjmsr-311 635 8 when when SCONJ bjmsr-311 635 9 probability probability NOUN bjmsr-311 635 10 density density NOUN bjmsr-311 635 11 function function NOUN bjmsr-311 635 12 is be AUX bjmsr-311 635 13 known know VERB bjmsr-311 635 14 . . PUNCT bjmsr-311 636 1 bijan bijan PROPN bjmsr-311 636 2 bidabad bidabad NOUN bjmsr-311 636 3 ( ( PUNCT bjmsr-311 636 4 2005 2005 NUM bjmsr-311 636 5 ) ) PUNCT bjmsr-311 636 6 . . PUNCT bjmsr-311 637 1 usa usa PROPN bjmsr-311 637 2 income income PROPN bjmsr-311 637 3 distribution distribution PROPN bjmsr-311 637 4 counter counter NOUN bjmsr-311 637 5 - - NOUN bjmsr-311 637 6 business business NOUN bjmsr-311 637 7 - - PUNCT bjmsr-311 637 8 cyclical cyclical ADJ bjmsr-311 637 9 trend trend NOUN bjmsr-311 637 10 ( ( PUNCT bjmsr-311 637 11 estimating estimate VERB bjmsr-311 637 12 lorenz lorenz PROPN bjmsr-311 637 13 curve curve NOUN bjmsr-311 637 14 using use VERB bjmsr-311 637 15 continuous continuous ADJ bjmsr-311 637 16 l1 l1 PROPN bjmsr-311 637 17 norm norm NOUN bjmsr-311 637 18 estimation estimation PROPN bjmsr-311 637 19 ) ) PUNCT bjmsr-311 637 20 . . PUNCT bjmsr-311 638 1 first first ADJ bjmsr-311 638 2 meeting meeting NOUN bjmsr-311 638 3 of of ADP bjmsr-311 638 4 the the DET bjmsr-311 638 5 society society NOUN bjmsr-311 638 6 for for ADP bjmsr-311 638 7 the the DET bjmsr-311 638 8 study study NOUN bjmsr-311 638 9 of of ADP bjmsr-311 638 10 economic economic ADJ bjmsr-311 638 11 inequality inequality NOUN bjmsr-311 638 12 ( ( PUNCT bjmsr-311 638 13 ecineq ecineq PROPN bjmsr-311 638 14 ) ) PUNCT bjmsr-311 638 15 , , PUNCT bjmsr-311 638 16 palma palma PROPN bjmsr-311 638 17 de de PROPN bjmsr-311 638 18 mallorca mallorca PROPN bjmsr-311 638 19 , , PUNCT bjmsr-311 638 20 spain spain PROPN bjmsr-311 638 21 , , PUNCT bjmsr-311 638 22 july july PROPN bjmsr-311 638 23 20 20 NUM bjmsr-311 638 24 - - SYM bjmsr-311 638 25 22 22 NUM bjmsr-311 638 26 , , PUNCT bjmsr-311 638 27 2005 2005 NUM bjmsr-311 638 28 . . PUNCT bjmsr-311 639 1 http://www.uib.es/congres/ecopub/ecineq/general.html http://www.uib.es/congres/ecopub/ecineq/general.html PROPN bjmsr-311 639 2 http://www.uib.es/congres/ecopub/ecineq/papers/039bidabab.pdf http://www.uib.es/congres/ecopub/ecineq/papers/039bidabab.pdf PROPN bjmsr-311 639 3 http://www.bidabad.com/doc/estimating-lorenz-us.pdf http://www.bidabad.com/doc/estimating-lorenz-us.pdf PROPN bjmsr-311 639 4 bijan bijan PROPN bjmsr-311 639 5 bidabad bidabad PROPN bjmsr-311 639 6 , , PUNCT bjmsr-311 639 7 hamid hamid PROPN bjmsr-311 639 8 shahrestani shahrestani PROPN bjmsr-311 639 9 . . PUNCT bjmsr-311 640 1 ( ( PUNCT bjmsr-311 640 2 2008 2008 NUM bjmsr-311 640 3 ) ) PUNCT bjmsr-311 640 4 an an DET bjmsr-311 640 5 implied imply VERB bjmsr-311 640 6 inequality inequality NOUN bjmsr-311 640 7 index index NOUN bjmsr-311 640 8 using use VERB bjmsr-311 640 9 l1 l1 PROPN bjmsr-311 640 10 norm norm NOUN bjmsr-311 640 11 estimation estimation NOUN bjmsr-311 640 12 of of ADP bjmsr-311 640 13 lorenz lorenz PROPN bjmsr-311 640 14 curve curve PROPN bjmsr-311 640 15 . . PUNCT bjmsr-311 641 1 global global ADJ bjmsr-311 641 2 conference conference NOUN bjmsr-311 641 3 on on ADP bjmsr-311 641 4 business business NOUN bjmsr-311 641 5 and and CCONJ bjmsr-311 641 6 finance finance NOUN bjmsr-311 641 7 proceedings proceeding NOUN bjmsr-311 641 8 . . PUNCT bjmsr-311 642 1 mercedes mercede NOUN bjmsr-311 642 2 jalbert jalbert PROPN bjmsr-311 642 3 , , PUNCT bjmsr-311 642 4 managing managing NOUN bjmsr-311 642 5 editor editor NOUN bjmsr-311 642 6 , , PUNCT bjmsr-311 642 7 issn issn PROPN bjmsr-311 642 8 1931 1931 NUM bjmsr-311 642 9 - - SYM bjmsr-311 642 10 0285 0285 NUM bjmsr-311 642 11 cd cd PROPN bjmsr-311 642 12 , , PUNCT bjmsr-311 642 13 issn issn PROPN bjmsr-311 642 14 1941 1941 NUM bjmsr-311 642 15 - - SYM bjmsr-311 642 16 9589 9589 NUM bjmsr-311 642 17 online online NOUN bjmsr-311 642 18 , , PUNCT bjmsr-311 642 19 volume volume NOUN bjmsr-311 642 20 3 3 NUM bjmsr-311 642 21 , , PUNCT bjmsr-311 642 22 number number NOUN bjmsr-311 642 23 2 2 NUM bjmsr-311 642 24 , , PUNCT bjmsr-311 642 25 2008 2008 NUM bjmsr-311 642 26 , , PUNCT bjmsr-311 642 27 the the DET bjmsr-311 642 28 institute institute NOUN bjmsr-311 642 29 for for ADP bjmsr-311 642 30 business business NOUN bjmsr-311 642 31 and and CCONJ bjmsr-311 642 32 finance finance NOUN bjmsr-311 642 33 research research NOUN bjmsr-311 642 34 , , PUNCT bjmsr-311 642 35 ramada ramada PROPN bjmsr-311 642 36 plaza plaza PROPN bjmsr-311 642 37 herradura herradura NOUN bjmsr-311 642 38 , , PUNCT bjmsr-311 642 39 san san PROPN bjmsr-311 642 40 jose jose PROPN bjmsr-311 642 41 , , PUNCT bjmsr-311 642 42 costa costa PROPN bjmsr-311 642 43 rica rica PROPN bjmsr-311 642 44 , , PUNCT bjmsr-311 642 45 may may AUX bjmsr-311 642 46 28 28 NUM bjmsr-311 642 47 - - SYM bjmsr-311 642 48 31 31 NUM bjmsr-311 642 49 , , PUNCT bjmsr-311 642 50 2008 2008 NUM bjmsr-311 642 51 , , PUNCT bjmsr-311 642 52 pp pp ADJ bjmsr-311 642 53 . . PUNCT bjmsr-311 643 1 148 148 NUM bjmsr-311 643 2 - - SYM bjmsr-311 643 3 163 163 NUM bjmsr-311 643 4 . . PUNCT bjmsr-311 644 1 global global ADJ bjmsr-311 644 2 journal journal PROPN bjmsr-311 644 3 of of ADP bjmsr-311 644 4 business business NOUN bjmsr-311 644 5 research research NOUN bjmsr-311 644 6 , , PUNCT bjmsr-311 644 7 vol vol NOUN bjmsr-311 644 8 . . PROPN bjmsr-311 644 9 4 4 NUM bjmsr-311 644 10 , , PUNCT bjmsr-311 644 11 no no INTJ bjmsr-311 644 12 . . NOUN bjmsr-311 644 13 1 1 NUM bjmsr-311 644 14 , , PUNCT bjmsr-311 644 15 2010 2010 NUM bjmsr-311 644 16 , , PUNCT bjmsr-311 644 17 pp.29 pp.29 NOUN bjmsr-311 644 18 - - PUNCT bjmsr-311 644 19 45 45 NUM bjmsr-311 644 20 . . PUNCT bjmsr-311 645 1 http://www.bidabad.com/doc/l1-implied-inequality-index-4.pdf http://www.bidabad.com/doc/l1-implied-inequality-index-4.pdf PROPN bjmsr-311 645 2 http://www.theibfr.com/archive/issn-1941-9589-v3-n2-2008.pdf http://www.theibfr.com/archive/issn-1941-9589-v3-n2-2008.pdf PROPN bjmsr-311 645 3 http://www.bidabad.com/doc/ssrn-id1631861.pdf http://www.bidabad.com/doc/ssrn-id1631861.pdf PROPN bjmsr-311 645 4 p. p. PROPN bjmsr-311 645 5 bloomfield bloomfield PROPN bjmsr-311 645 6 , , PUNCT bjmsr-311 645 7 w. w. PROPN bjmsr-311 645 8 steiger steiger PROPN bjmsr-311 645 9 ( ( PUNCT bjmsr-311 645 10 1980 1980 NUM bjmsr-311 645 11 ) ) PUNCT bjmsr-311 645 12 least least ADJ bjmsr-311 645 13 absolute absolute ADJ bjmsr-311 645 14 deviations deviation NOUN bjmsr-311 645 15 curve curve VERB bjmsr-311 645 16 fitting fitting ADJ bjmsr-311 645 17 . . PUNCT bjmsr-311 646 1 siam siam PROPN bjmsr-311 646 2 j. j. PROPN bjmsr-311 646 3 sci sci PROPN bjmsr-311 646 4 . . PROPN bjmsr-311 646 5 stat stat PROPN bjmsr-311 646 6 . . PUNCT bjmsr-311 647 1 comput comput NOUN bjmsr-311 647 2 . . PUNCT bjmsr-311 648 1 1 1 NUM bjmsr-311 648 2 , , PUNCT bjmsr-311 648 3 290 290 NUM bjmsr-311 648 4 - - SYM bjmsr-311 648 5 301 301 NUM bjmsr-311 648 6 . . PUNCT bjmsr-311 649 1 r.j r.j PROPN bjmsr-311 649 2 . . PROPN bjmsr-311 649 3 boscovich boscovich PROPN bjmsr-311 649 4 ( ( PUNCT bjmsr-311 649 5 1757 1757 NUM bjmsr-311 649 6 ) ) PUNCT bjmsr-311 649 7 de de X bjmsr-311 649 8 litteraria litteraria X bjmsr-311 649 9 expeditione expeditione NOUN bjmsr-311 649 10 per per ADP bjmsr-311 649 11 pontificiam pontificiam PROPN bjmsr-311 649 12 ditionem ditionem PROPN bjmsr-311 649 13 , , PUNCT bjmsr-311 649 14 et et PROPN bjmsr-311 649 15 synopsis synopsis PROPN bjmsr-311 649 16 amplioris amplioris PROPN bjmsr-311 649 17 operis operis PROPN bjmsr-311 649 18 ... ... PUNCT bjmsr-311 649 19 , , PUNCT bjmsr-311 649 20 ' ' PUNCT bjmsr-311 649 21 bononiensi bononiensi VERB bjmsr-311 649 22 ' ' PUNCT bjmsr-311 649 23 scientiarum scientiarum PROPN bjmsr-311 649 24 et et PROPN bjmsr-311 649 25 artum artum PROPN bjmsr-311 649 26 instituto instituto PROPN bjmsr-311 649 27 atque atque PROPN bjmsr-311 649 28 academia academia PROPN bjmsr-311 649 29 commetarii commetarii PROPN bjmsr-311 649 30 , , PUNCT bjmsr-311 649 31 vol.4 vol.4 PROPN bjmsr-311 649 32 , , PUNCT bjmsr-311 649 33 353 353 NUM bjmsr-311 649 34 - - SYM bjmsr-311 649 35 396 396 NUM bjmsr-311 649 36 . . PUNCT bjmsr-311 650 1 reprinted reprint VERB bjmsr-311 650 2 with with ADP bjmsr-311 650 3 a a DET bjmsr-311 650 4 serbo serbo NOUN bjmsr-311 650 5 - - ADJ bjmsr-311 650 6 croatian croatian ADJ bjmsr-311 650 7 translation translation NOUN bjmsr-311 650 8 by by ADP bjmsr-311 650 9 n. n. PROPN bjmsr-311 650 10 cubranic cubranic PROPN bjmsr-311 650 11 , , PUNCT bjmsr-311 650 12 institute institute NOUN bjmsr-311 650 13 of of ADP bjmsr-311 650 14 higher high ADJ bjmsr-311 650 15 geodesy geodesy PROPN bjmsr-311 650 16 , , PUNCT bjmsr-311 650 17 university university NOUN bjmsr-311 650 18 of of ADP bjmsr-311 650 19 zagreb zagreb PROPN bjmsr-311 650 20 1961 1961 NUM bjmsr-311 650 21 . . PUNCT bjmsr-311 651 1 j. j. PROPN bjmsr-311 651 2 chambers chambers PROPN bjmsr-311 651 3 ( ( PUNCT bjmsr-311 651 4 1971 1971 NUM bjmsr-311 651 5 ) ) PUNCT bjmsr-311 651 6 algorithm algorithm NOUN bjmsr-311 651 7 410 410 NUM bjmsr-311 651 8 : : PUNCT bjmsr-311 651 9 partial partial ADJ bjmsr-311 651 10 sorting sorting NOUN bjmsr-311 651 11 . . PUNCT bjmsr-311 652 1 comm comm NOUN bjmsr-311 652 2 . . PUNCT bjmsr-311 653 1 acm acm PROPN bjmsr-311 653 2 , , PUNCT bjmsr-311 653 3 14 14 NUM bjmsr-311 653 4 , , PUNCT bjmsr-311 653 5 357 357 NUM bjmsr-311 653 6 - - SYM bjmsr-311 653 7 358 358 NUM bjmsr-311 653 8 . . PUNCT bjmsr-311 654 1 f.h f.h PROPN bjmsr-311 654 2 . . PROPN bjmsr-311 654 3 clarke clarke PROPN bjmsr-311 654 4 ( ( PUNCT bjmsr-311 654 5 1983 1983 NUM bjmsr-311 654 6 ) ) PUNCT bjmsr-311 654 7 optimization optimization NOUN bjmsr-311 654 8 and and CCONJ bjmsr-311 654 9 nonsmooth nonsmooth ADJ bjmsr-311 654 10 analysis analysis NOUN bjmsr-311 654 11 . . PUNCT bjmsr-311 655 1 wiley wiley PROPN bjmsr-311 655 2 , , PUNCT bjmsr-311 655 3 new new PROPN bjmsr-311 655 4 york york PROPN bjmsr-311 655 5 c.a.r c.a.r PROPN bjmsr-311 655 6 . . PUNCT bjmsr-311 656 1 hoare hoare PROPN bjmsr-311 656 2 ( ( PUNCT bjmsr-311 656 3 1961 1961 NUM bjmsr-311 656 4 ) ) PUNCT bjmsr-311 656 5 algorithm algorithm NOUN bjmsr-311 656 6 63 63 NUM bjmsr-311 656 7 partition partition NOUN bjmsr-311 656 8 ; ; PUNCT bjmsr-311 656 9 64 64 NUM bjmsr-311 656 10 , , PUNCT bjmsr-311 656 11 quicksort quicksort NOUN bjmsr-311 656 12 ; ; PUNCT bjmsr-311 656 13 and and CCONJ bjmsr-311 656 14 65 65 NUM bjmsr-311 656 15 , , PUNCT bjmsr-311 656 16 find find VERB bjmsr-311 656 17 . . PUNCT bjmsr-311 656 18 , , PUNCT bjmsr-311 657 1 comm comm NOUN bjmsr-311 657 2 . . PUNCT bjmsr-311 657 3 acm acm PROPN bjmsr-311 657 4 , , PUNCT bjmsr-311 657 5 4 4 NUM bjmsr-311 657 6 , , PUNCT bjmsr-311 657 7 july july PROPN bjmsr-311 657 8 , , PUNCT bjmsr-311 657 9 321 321 NUM bjmsr-311 657 10 - - SYM bjmsr-311 657 11 322 322 NUM bjmsr-311 657 12 . . PUNCT bjmsr-311 657 13 c.a.r c.a.r NOUN bjmsr-311 657 14 . . PUNCT bjmsr-311 658 1 hoare hoare PROPN bjmsr-311 658 2 ( ( PUNCT bjmsr-311 658 3 1962 1962 NUM bjmsr-311 658 4 ) ) PUNCT bjmsr-311 658 5 quicksort quicksort NOUN bjmsr-311 658 6 . . PUNCT bjmsr-311 659 1 comput comput PROPN bjmsr-311 659 2 . . PUNCT bjmsr-311 660 1 j. j. PROPN bjmsr-311 660 2 , , PUNCT bjmsr-311 660 3 5 5 NUM bjmsr-311 660 4 , , PUNCT bjmsr-311 660 5 10 10 NUM bjmsr-311 660 6 - - SYM bjmsr-311 660 7 15 15 NUM bjmsr-311 660 8 . . PUNCT bjmsr-311 661 1 o.j o.j PROPN bjmsr-311 661 2 . . PROPN bjmsr-311 661 3 karst karst PROPN bjmsr-311 661 4 ( ( PUNCT bjmsr-311 661 5 1958 1958 NUM bjmsr-311 661 6 ) ) PUNCT bjmsr-311 661 7 linear linear NOUN bjmsr-311 661 8 curve curve NOUN bjmsr-311 661 9 fitting fitting ADJ bjmsr-311 661 10 using use VERB bjmsr-311 661 11 least least ADJ bjmsr-311 661 12 deviations deviation NOUN bjmsr-311 661 13 . . PUNCT bjmsr-311 662 1 jasa jasa PROPN bjmsr-311 662 2 , , PUNCT bjmsr-311 662 3 53 53 NUM bjmsr-311 662 4 , , PUNCT bjmsr-311 662 5 118 118 NUM bjmsr-311 662 6 - - SYM bjmsr-311 662 7 132 132 NUM bjmsr-311 662 8 . . PUNCT bjmsr-311 663 1 p.s p.s PROPN bjmsr-311 663 2 . . PROPN bjmsr-311 663 3 laplace laplace PROPN bjmsr-311 663 4 ( ( PUNCT bjmsr-311 663 5 1812 1812 NUM bjmsr-311 663 6 ) ) PUNCT bjmsr-311 663 7 theorie theorie PROPN bjmsr-311 663 8 analytique analytique PROPN bjmsr-311 663 9 des des X bjmsr-311 663 10 probabilites probabilite NOUN bjmsr-311 663 11 , , PUNCT bjmsr-311 663 12 mme mme X bjmsr-311 663 13 courcier courcier PROPN bjmsr-311 663 14 paris paris PROPN bjmsr-311 663 15 1820 1820 NUM bjmsr-311 663 16 reprinted reprint VERB bjmsr-311 663 17 in in ADP bjmsr-311 663 18 his his PRON bjmsr-311 663 19 oeuvres oeuvre NOUN bjmsr-311 663 20 , , PUNCT bjmsr-311 663 21 vol.7 vol.7 PROPN bjmsr-311 663 22 , , PUNCT bjmsr-311 663 23 imprimerie imprimerie PROPN bjmsr-311 663 24 royale royale PROPN bjmsr-311 663 25 , , PUNCT bjmsr-311 663 26 paris paris PROPN bjmsr-311 663 27 , , PUNCT bjmsr-311 663 28 1847 1847 NUM bjmsr-311 663 29 , , PUNCT bjmsr-311 663 30 and and CCONJ bjmsr-311 663 31 gauthier gauthier NOUN bjmsr-311 663 32 - - PUNCT bjmsr-311 663 33 villars villar NOUN bjmsr-311 663 34 et et NOUN bjmsr-311 663 35 fils fil NOUN bjmsr-311 663 36 , , PUNCT bjmsr-311 663 37 paris paris PROPN bjmsr-311 663 38 1886 1886 NUM bjmsr-311 663 39 . . PUNCT bjmsr-311 664 1 p.s p.s PROPN bjmsr-311 664 2 . . PROPN bjmsr-311 664 3 laplace laplace PROPN bjmsr-311 664 4 ( ( PUNCT bjmsr-311 664 5 1818 1818 NUM bjmsr-311 664 6 ) ) PUNCT bjmsr-311 664 7 duexieme duexieme NOUN bjmsr-311 664 8 supplement supplement NOUN bjmsr-311 664 9 to to ADP bjmsr-311 664 10 laplace laplace NOUN bjmsr-311 664 11 ( ( PUNCT bjmsr-311 664 12 1812 1812 NUM bjmsr-311 664 13 ) ) PUNCT bjmsr-311 664 14 . . PUNCT bjmsr-311 665 1 s. s. PROPN bjmsr-311 665 2 scowen scowen PROPN bjmsr-311 665 3 ( ( PUNCT bjmsr-311 665 4 1965 1965 NUM bjmsr-311 665 5 ) ) PUNCT bjmsr-311 665 6 algorithm algorithm NOUN bjmsr-311 665 7 271 271 NUM bjmsr-311 665 8 quickersort quickersort NOUN bjmsr-311 665 9 . . PUNCT bjmsr-311 666 1 comm comm NOUN bjmsr-311 666 2 . . PUNCT bjmsr-311 666 3 acm acm PROPN bjmsr-311 666 4 , , PUNCT bjmsr-311 666 5 8 8 NUM bjmsr-311 666 6 , , PUNCT bjmsr-311 666 7 669 669 NUM bjmsr-311 666 8 - - SYM bjmsr-311 666 9 670 670 NUM bjmsr-311 666 10 . . PUNCT bjmsr-311 667 1 r.s r.s PROPN bjmsr-311 667 2 . . PROPN bjmsr-311 667 3 singleton singleton PROPN bjmsr-311 667 4 ( ( PUNCT bjmsr-311 667 5 1969 1969 NUM bjmsr-311 667 6 ) ) PUNCT bjmsr-311 667 7 algorithm algorithm NOUN bjmsr-311 667 8 347 347 NUM bjmsr-311 667 9 sort sort NOUN bjmsr-311 667 10 . . PUNCT bjmsr-311 668 1 comm comm NOUN bjmsr-311 668 2 . . PUNCT bjmsr-311 668 3 acm acm PROPN bjmsr-311 668 4 , , PUNCT bjmsr-311 668 5 12 12 NUM bjmsr-311 668 6 , , PUNCT bjmsr-311 668 7 185 185 NUM bjmsr-311 668 8 - - SYM bjmsr-311 668 9 186 186 NUM bjmsr-311 668 10 . . PUNCT bjmsr-311 669 1 l.d l.d PROPN bjmsr-311 669 2 . . PROPN bjmsr-311 669 3 taylor taylor PROPN bjmsr-311 669 4 ( ( PUNCT bjmsr-311 669 5 1974 1974 NUM bjmsr-311 669 6 ) ) PUNCT bjmsr-311 669 7 estimating estimate VERB bjmsr-311 669 8 by by ADP bjmsr-311 669 9 minimizing minimize VERB bjmsr-311 669 10 the the DET bjmsr-311 669 11 sum sum NOUN bjmsr-311 669 12 of of ADP bjmsr-311 669 13 absolute absolute ADJ bjmsr-311 669 14 errors error NOUN bjmsr-311 669 15 . . PUNCT bjmsr-311 670 1 in in ADP bjmsr-311 670 2 p. p. PROPN bjmsr-311 670 3 zarembka zarembka PROPN bjmsr-311 670 4 ( ( PUNCT bjmsr-311 670 5 ed ed NOUN bjmsr-311 670 6 . . PUNCT bjmsr-311 670 7 ) ) PUNCT bjmsr-311 671 1 frontiers frontier NOUN bjmsr-311 671 2 in in ADP bjmsr-311 671 3 econometrics econometric NOUN bjmsr-311 671 4 . . PUNCT bjmsr-311 672 1 academic academic ADJ bjmsr-311 672 2 press press NOUN bjmsr-311 672 3 . . PUNCT bjmsr-311 673 1 copyrights copyright VERB bjmsr-311 673 2 copyright copyright NOUN bjmsr-311 673 3 for for ADP bjmsr-311 673 4 this this DET bjmsr-311 673 5 article article NOUN bjmsr-311 673 6 is be AUX bjmsr-311 673 7 retained retain VERB bjmsr-311 673 8 by by ADP bjmsr-311 673 9 the the DET bjmsr-311 673 10 author(s author(s PROPN bjmsr-311 673 11 ) ) PUNCT bjmsr-311 673 12 , , PUNCT bjmsr-311 673 13 with with ADP bjmsr-311 673 14 first first ADJ bjmsr-311 673 15 publication publication NOUN bjmsr-311 673 16 rights right NOUN bjmsr-311 673 17 granted grant VERB bjmsr-311 673 18 to to ADP bjmsr-311 673 19 the the DET bjmsr-311 673 20 journal journal NOUN bjmsr-311 673 21 . . PUNCT bjmsr-311 674 1 this this PRON bjmsr-311 674 2 is be AUX bjmsr-311 674 3 an an DET bjmsr-311 674 4 open open ADJ bjmsr-311 674 5 - - PUNCT bjmsr-311 674 6 access access NOUN bjmsr-311 674 7 article article NOUN bjmsr-311 674 8 distributed distribute VERB bjmsr-311 674 9 under under ADP bjmsr-311 674 10 the the DET bjmsr-311 674 11 terms term NOUN bjmsr-311 674 12 and and CCONJ bjmsr-311 674 13 conditions condition NOUN bjmsr-311 674 14 of of ADP bjmsr-311 674 15 the the DET bjmsr-311 674 16 creative creative ADJ bjmsr-311 674 17 commons common NOUN bjmsr-311 674 18 attribution attribution NOUN bjmsr-311 674 19 license license NOUN bjmsr-311 674 20 ( ( PUNCT bjmsr-311 674 21 http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/ PROPN bjmsr-311 674 22 ) ) PUNCT bjmsr-311 674 23 . . PUNCT bjmsr-311 675 1 http://www.bidabad.com/doc/l1-norm-thesis-en.pdf http://www.bidabad.com/doc/l1-norm-thesis-en.pdf PROPN bjmsr-311 675 2 http://www.bidabad.com/doc/l1-norm-thesis-fa.pdf http://www.bidabad.com/doc/l1-norm-thesis-fa.pdf PROPN bjmsr-311 675 3 http://www.bidabad.com/doc/l1-article6.pdf http://www.bidabad.com/doc/l1-article6.pdf PROPN bjmsr-311 675 4 http://www.bidabad.com/doc/l1-article5.pdf http://www.bidabad.com/doc/l1-article5.pdf PROPN bjmsr-311 675 5 http://www.bidabad.com/doc/l1-article5.pdf http://www.bidabad.com/doc/l1-article5.pdf PROPN bjmsr-311 675 6 http://www.bidabad.com/doc/l1-article1.pdf http://www.bidabad.com/doc/l1-article1.pdf PROPN bjmsr-311 675 7 http://www.bidabad.com/doc/l1-article2.pdf http://www.bidabad.com/doc/l1-article2.pdf PROPN bjmsr-311 675 8 http://www.bidabad.com/doc/l1-article3.pdf http://www.bidabad.com/doc/l1-article3.pdf PROPN bjmsr-311 675 9 http://www.bidabad.com/doc/l1-article3.pdf http://www.bidabad.com/doc/l1-article3.pdf PROPN bjmsr-311 675 10 http://www.bidabad.com/doc/l1-article4.pdf http://www.bidabad.com/doc/l1-article4.pdf PROPN bjmsr-311 675 11 http://www.bidabad.com/doc/iraninc-l1.pdf http://www.bidabad.com/doc/iraninc-l1.pdf PROPN bjmsr-311 675 12 http://www.uib.es/congres/ecopub/ecineq/general.htm http://www.uib.es/congres/ecopub/ecineq/general.htm DET bjmsr-311 675 13 http://www.uib.es/congres/ecopub/ecineq/papers/039bidabab.pdf http://www.uib.es/congres/ecopub/ecineq/papers/039bidabab.pdf PROPN bjmsr-311 675 14 http://www.bidabad.com/doc/estimating-lorenz-us.pdf http://www.bidabad.com/doc/estimating-lorenz-us.pdf PROPN bjmsr-311 675 15 http://www.bidabad.com/doc/l1-implied-inequality-index-4.pdf http://www.bidabad.com/doc/l1-implied-inequality-index-4.pdf PROPN bjmsr-311 675 16 http://www.theibfr.com/archive/issn-1941-9589-v3-n2-2008.pdf http://www.theibfr.com/archive/issn-1941-9589-v3-n2-2008.pdf PROPN bjmsr-311 675 17 http://www.bidabad.com/doc/ssrn-id1631861.pdf http://www.bidabad.com/doc/ssrn-id1631861.pdf PROPN