id sid tid token lemma pos hjic-1073 1 1 hungarian hungarian ADJ hjic-1073 1 2 journal journal NOUN hjic-1073 1 3 of of ADP hjic-1073 1 4 lndustrial lndustrial ADJ hjic-1073 1 5 chemistry chemistry NOUN hjic-1073 1 6 veszprem veszprem NOUN hjic-1073 1 7 vol vol NOUN hjic-1073 1 8 . . PROPN hjic-1073 2 1 29 29 NUM hjic-1073 2 2 . . PUNCT hjic-1073 3 1 pp pp ADJ hjic-1073 3 2 . . PUNCT hjic-1073 4 1 67 67 NUM hjic-1073 4 2 - - SYM hjic-1073 4 3 70 70 NUM hjic-1073 4 4 ( ( PUNCT hjic-1073 4 5 2001 2001 NUM hjic-1073 4 6 ) ) PUNCT hjic-1073 4 7 least least ADJ hjic-1073 4 8 squares square NOUN hjic-1073 4 9 and and CCONJ hjic-1073 4 10 the the DET hjic-1073 4 11 matrix matrix NOUN hjic-1073 4 12 riccati riccati PROPN hjic-1073 4 13 equation equation PROPN hjic-1073 4 14 c. c. PROPN hjic-1073 4 15 storey storey PROPN hjic-1073 4 16 ( ( PUNCT hjic-1073 4 17 the the DET hjic-1073 4 18 institute institute PROPN hjic-1073 4 19 of of ADP hjic-1073 4 20 mathematics mathematics PROPN hjic-1073 4 21 and and CCONJ hjic-1073 4 22 simulation simulation NOUN hjic-1073 4 23 sciences sciences PROPN hjic-1073 4 24 , , PUNCT hjic-1073 4 25 faculty faculty NOUN hjic-1073 4 26 of of ADP hjic-1073 4 27 computing compute VERB hjic-1073 4 28 sciences science NOUN hjic-1073 4 29 and and CCONJ hjic-1073 4 30 engineering engineering NOUN hjic-1073 4 31 , , PUNCT hjic-1073 4 32 de de PROPN hjic-1073 4 33 montfort montfort PROPN hjic-1073 4 34 university university PROPN hjic-1073 4 35 , , PUNCT hjic-1073 4 36 the the DET hjic-1073 4 37 gateway gateway NOUN hjic-1073 4 38 , , PUNCT hjic-1073 4 39 leicester leicester NOUN hjic-1073 4 40 , , PUNCT hjic-1073 4 41 lei lei PROPN hjic-1073 4 42 9bh 9bh NOUN hjic-1073 4 43 , , PUNCT hjic-1073 4 44 uk uk PROPN hjic-1073 4 45 ) ) PUNCT hjic-1073 4 46 received receive VERB hjic-1073 4 47 : : PUNCT hjic-1073 4 48 july july PROPN hjic-1073 4 49 26 26 NUM hjic-1073 4 50 , , PUNCT hjic-1073 4 51 2001 2001 NUM hjic-1073 4 52 there there PRON hjic-1073 4 53 are be VERB hjic-1073 4 54 a a DET hjic-1073 4 55 number number NOUN hjic-1073 4 56 of of ADP hjic-1073 4 57 methods method NOUN hjic-1073 4 58 for for ADP hjic-1073 4 59 least least ADJ hjic-1073 4 60 squares square NOUN hjic-1073 4 61 and and CCONJ hjic-1073 4 62 total total ADJ hjic-1073 4 63 least least ADJ hjic-1073 4 64 squares square NOUN hjic-1073 4 65 solution solution NOUN hjic-1073 4 66 of of ADP hjic-1073 4 67 linear linear PROPN hjic-1073 4 68 equations equation NOUN hjic-1073 4 69 . . PUNCT hjic-1073 5 1 one one NUM hjic-1073 5 2 such such ADJ hjic-1073 5 3 method method NOUN hjic-1073 5 4 involves involve VERB hjic-1073 5 5 solving solve VERB hjic-1073 5 6 an an DET hjic-1073 5 7 appropriate appropriate ADJ hjic-1073 5 8 algebraic algebraic ADJ hjic-1073 5 9 matrix matrix NOUN hjic-1073 5 10 riccati riccati NOUN hjic-1073 5 11 equation equation NOUN hjic-1073 5 12 . . PUNCT hjic-1073 6 1 this this DET hjic-1073 6 2 approach approach NOUN hjic-1073 6 3 is be AUX hjic-1073 6 4 investigated investigate VERB hjic-1073 6 5 here here ADV hjic-1073 6 6 using use VERB hjic-1073 6 7 an an DET hjic-1073 6 8 algorithm algorithm NOUN hjic-1073 6 9 based base VERB hjic-1073 6 10 on on ADP hjic-1073 6 11 newton newton PROPN hjic-1073 6 12 's 's PART hjic-1073 6 13 method method NOUN hjic-1073 6 14 with with ADP hjic-1073 6 15 an an DET hjic-1073 6 16 infinite infinite ADJ hjic-1073 6 17 series series NOUN hjic-1073 6 18 solution solution NOUN hjic-1073 6 19 of of ADP hjic-1073 6 20 the the DET hjic-1073 6 21 resulting result VERB hjic-1073 6 22 linear linear ADJ hjic-1073 6 23 matrix matrix NOUN hjic-1073 6 24 equations equation NOUN hjic-1073 6 25 . . PUNCT hjic-1073 7 1 some some DET hjic-1073 7 2 numerical numerical ADJ hjic-1073 7 3 examples example NOUN hjic-1073 7 4 , , PUNCT hjic-1073 7 5 from from ADP hjic-1073 7 6 the the DET hjic-1073 7 7 recent recent ADJ hjic-1073 7 8 literature literature NOUN hjic-1073 7 9 , , PUNCT hjic-1073 7 10 are be AUX hjic-1073 7 11 used use VERB hjic-1073 7 12 to to PART hjic-1073 7 13 illustrate illustrate VERB hjic-1073 7 14 the the DET hjic-1073 7 15 techniques technique NOUN hjic-1073 7 16 . . PUNCT hjic-1073 8 1 keywords keyword NOUN hjic-1073 8 2 : : PUNCT hjic-1073 8 3 matrix matrix NOUN hjic-1073 8 4 riccati riccati NOUN hjic-1073 8 5 equation equation NOUN hjic-1073 8 6 ; ; PUNCT hjic-1073 8 7 newton newton PROPN hjic-1073 8 8 's 's PART hjic-1073 8 9 method method NOUN hjic-1073 8 10 ; ; PUNCT hjic-1073 8 11 infinite infinite ADJ hjic-1073 8 12 series series NOUN hjic-1073 8 13 solution solution NOUN hjic-1073 8 14 ; ; PUNCT hjic-1073 8 15 overdetermined overdetermine VERB hjic-1073 8 16 linear linear PROPN hjic-1073 8 17 systems system NOUN hjic-1073 8 18 ; ; PUNCT hjic-1073 8 19 least least ADJ hjic-1073 8 20 squares square NOUN hjic-1073 8 21 and and CCONJ hjic-1073 8 22 total total ADJ hjic-1073 8 23 least least ADJ hjic-1073 8 24 squares square NOUN hjic-1073 8 25 . . PUNCT hjic-1073 9 1 introduction introduction NOUN hjic-1073 9 2 when when SCONJ hjic-1073 9 3 a a DET hjic-1073 9 4 system system NOUN hjic-1073 9 5 of of ADP hjic-1073 9 6 linear linear PROPN hjic-1073 9 7 equations equation NOUN hjic-1073 9 8 ( ( PUNCT hjic-1073 9 9 1 1 NUM hjic-1073 9 10 ) ) PUNCT hjic-1073 9 11 with with ADP hjic-1073 9 12 land land NOUN hjic-1073 9 13 m m PROPN hjic-1073 9 14 , , PUNCT hjic-1073 9 15 m m VERB hjic-1073 9 16 x x NOUN hjic-1073 9 17 nand nand NOUN hjic-1073 9 18 m m PROPN hjic-1073 9 19 x x X hjic-1073 9 20 p p PRON hjic-1073 9 21 matrices matrix NOUN hjic-1073 9 22 respectively respectively ADV hjic-1073 9 23 , , PUNCT hjic-1073 9 24 does do AUX hjic-1073 9 25 not not PART hjic-1073 9 26 have have VERB hjic-1073 9 27 a a DET hjic-1073 9 28 unique unique ADJ hjic-1073 9 29 solution solution NOUN hjic-1073 9 30 x x INTJ hjic-1073 9 31 it it PRON hjic-1073 9 32 is be AUX hjic-1073 9 33 usual usual ADJ hjic-1073 9 34 to to PART hjic-1073 9 35 seek seek VERB hjic-1073 9 36 a a DET hjic-1073 9 37 solution solution NOUN hjic-1073 9 38 that that PRON hjic-1073 9 39 is be AUX hjic-1073 9 40 " " PUNCT hjic-1073 9 41 best good ADJ hjic-1073 9 42 " " PUNCT hjic-1073 9 43 in in ADP hjic-1073 9 44 some some DET hjic-1073 9 45 sense sense NOUN hjic-1073 9 46 by by ADP hjic-1073 9 47 imposing impose VERB hjic-1073 9 48 appropriate appropriate ADJ hjic-1073 9 49 constraints constraint NOUN hjic-1073 9 50 . . PUNCT hjic-1073 10 1 this this DET hjic-1073 10 2 paper paper NOUN hjic-1073 10 3 is be AUX hjic-1073 10 4 concerned concern VERB hjic-1073 10 5 with with ADP hjic-1073 10 6 computing compute VERB hjic-1073 10 7 the the DET hjic-1073 10 8 least least ADJ hjic-1073 10 9 squares square NOUN hjic-1073 10 10 ( ( PUNCT hjic-1073 10 11 ls ls ADJ hjic-1073 10 12 ) ) PUNCT hjic-1073 10 13 solution solution NOUN hjic-1073 10 14 , , PUNCT hjic-1073 10 15 which which PRON hjic-1073 10 16 imposes impose VERB hjic-1073 10 17 the the DET hjic-1073 10 18 constraint constraint NOUN hjic-1073 10 19 that that PRON hjic-1073 10 20 x x PRON hjic-1073 10 21 should should AUX hjic-1073 10 22 minimize minimize VERB hjic-1073 10 23 the the DET hjic-1073 10 24 norm norm NOUN hjic-1073 10 25 ! ! PUNCT hjic-1073 11 1 ilx ilx PROPN hjic-1073 11 2 mjj~ mjj~ PROPN hjic-1073 11 3 , , PUNCT hjic-1073 11 4 and and CCONJ hjic-1073 11 5 the the DET hjic-1073 11 6 total total ADJ hjic-1073 11 7 least least ADJ hjic-1073 11 8 squares square NOUN hjic-1073 11 9 ( ( PUNCT hjic-1073 11 10 tls tls PROPN hjic-1073 11 11 ) ) PUNCT hjic-1073 11 12 solution solution NOUN hjic-1073 11 13 which which PRON hjic-1073 11 14 requires require VERB hjic-1073 11 15 x x PUNCT hjic-1073 11 16 to to PART hjic-1073 11 17 minimize minimize VERB hjic-1073 11 18 illvjj~ illvjj~ PRON hjic-1073 11 19 + + CCONJ hjic-1073 11 20 jjm jjm PROPN hjic-1073 11 21 wjj~ wjj~ PROPN hjic-1073 11 22 subject subject NOUN hjic-1073 11 23 to to ADP hjic-1073 11 24 the the DET hjic-1073 11 25 constraint constraint NOUN hjic-1073 11 26 vx vx PROPN hjic-1073 11 27 = = PROPN hjic-1073 11 28 w. w. PROPN hjic-1073 11 29 ( ( PUNCT hjic-1073 11 30 2 2 NUM hjic-1073 11 31 ) ) PUNCT hjic-1073 11 32 the the DET hjic-1073 11 33 main main ADJ hjic-1073 11 34 difference difference NOUN hjic-1073 11 35 between between ADP hjic-1073 11 36 ls ls PROPN hjic-1073 11 37 and and CCONJ hjic-1073 11 38 tls tls PROPN hjic-1073 11 39 is be AUX hjic-1073 11 40 that that SCONJ hjic-1073 11 41 the the DET hjic-1073 11 42 former former ADJ hjic-1073 11 43 assumes assume VERB hjic-1073 11 44 the the DET hjic-1073 11 45 matrix matrix NOUN hjic-1073 11 46 l l NOUN hjic-1073 11 47 is be AUX hjic-1073 11 48 exact exact ADJ hjic-1073 11 49 whereas whereas SCONJ hjic-1073 11 50 the the DET hjic-1073 11 51 latter latter ADJ hjic-1073 11 52 allows allow VERB hjic-1073 11 53 for for ADP hjic-1073 11 54 errors error NOUN hjic-1073 11 55 in in ADP hjic-1073 11 56 both both DET hjic-1073 11 57 l l NOUN hjic-1073 11 58 and and CCONJ hjic-1073 11 59 m. m. NOUN hjic-1073 11 60 perhaps perhaps ADV hjic-1073 11 61 the the DET hjic-1073 11 62 most most ADV hjic-1073 11 63 important important ADJ hjic-1073 11 64 approach approach NOUN hjic-1073 11 65 in in ADP hjic-1073 11 66 solving solve VERB hjic-1073 11 67 these these DET hjic-1073 11 68 problems problem NOUN hjic-1073 11 69 is be AUX hjic-1073 11 70 singular singular ADJ hjic-1073 11 71 value value NOUN hjic-1073 11 72 decomposition decomposition NOUN hjic-1073 11 73 ( ( PUNCT hjic-1073 11 74 svd svd PROPN hjic-1073 11 75 ) ) PUNCT hjic-1073 11 76 the the DET hjic-1073 11 77 use use NOUN hjic-1073 11 78 of of ADP hjic-1073 11 79 which which PRON hjic-1073 11 80 is be AUX hjic-1073 11 81 fully fully ADV hjic-1073 11 82 discussed discuss VERB hjic-1073 11 83 in in ADP hjic-1073 11 84 [ [ X hjic-1073 11 85 1 1 NUM hjic-1073 11 86 ] ] PUNCT hjic-1073 11 87 and and CCONJ hjic-1073 11 88 [ [ X hjic-1073 11 89 2 2 NUM hjic-1073 11 90 } } PUNCT hjic-1073 11 91 for for ADP hjic-1073 11 92 ls ls PROPN hjic-1073 11 93 and and CCONJ hjic-1073 11 94 tls tls VERB hjic-1073 11 95 respectively respectively ADV hjic-1073 11 96 . . PUNCT hjic-1073 12 1 another another DET hjic-1073 12 2 possible possible ADJ hjic-1073 12 3 approach approach NOUN hjic-1073 12 4 is be AUX hjic-1073 12 5 the the DET hjic-1073 12 6 following following NOUN hjic-1073 12 7 . . PUNCT hjic-1073 13 1 by by ADP hjic-1073 13 2 using use VERB hjic-1073 13 3 lagrange lagrange NOUN hjic-1073 13 4 multipliers multiplier NOUN hjic-1073 13 5 , , PUNCT hjic-1073 13 6 in in ADP hjic-1073 13 7 the the DET hjic-1073 13 8 usual usual ADJ hjic-1073 13 9 way way NOUN hjic-1073 13 10 , , PUNCT hjic-1073 13 11 it it PRON hjic-1073 13 12 can can AUX hjic-1073 13 13 be be AUX hjic-1073 13 14 shown show VERB hjic-1073 13 15 [ [ PRON hjic-1073 13 16 3j 3j NUM hjic-1073 13 17 , , PUNCT hjic-1073 13 18 [ [ X hjic-1073 13 19 4 4 NUM hjic-1073 13 20 ] ] PUNCT hjic-1073 13 21 , , PUNCT hjic-1073 13 22 that that SCONJ hjic-1073 13 23 x x PRON hjic-1073 13 24 satisfies satisfy VERB hjic-1073 13 25 the the DET hjic-1073 13 26 algebraic algebraic ADJ hjic-1073 13 27 matrix matrix NOUN hjic-1073 13 28 riccati riccati NOUN hjic-1073 13 29 equation equation NOUN hjic-1073 13 30 ( ( PUNCT hjic-1073 13 31 amre amre PROPN hjic-1073 13 32 ) ) PUNCT hjic-1073 14 1 xm xm PROPN hjic-1073 15 1 t t PROPN hjic-1073 15 2 lx+ lx+ PROPN hjic-1073 16 1 lt lt DET hjic-1073 16 2 lxxm lxxm PROPN hjic-1073 16 3 t t PROPN hjic-1073 16 4 m m VERB hjic-1073 16 5 lt lt PRON hjic-1073 16 6 m m ADJ hjic-1073 16 7 = = ADJ hjic-1073 16 8 0 0 NUM hjic-1073 16 9 . . PUNCT hjic-1073 17 1 ( ( PUNCT hjic-1073 17 2 3 3 X hjic-1073 17 3 ) ) PUNCT hjic-1073 17 4 when when SCONJ hjic-1073 17 5 newton newton PROPN hjic-1073 17 6 's 's PART hjic-1073 17 7 method method NOUN hjic-1073 17 8 is be AUX hjic-1073 17 9 applied apply VERB hjic-1073 17 10 to to ADP hjic-1073 17 11 the the DET hjic-1073 17 12 general general ADJ hjic-1073 17 13 amre amre PROPN hjic-1073 17 14 xpx xpx PROPN hjic-1073 18 1 + + PROPN hjic-1073 18 2 qx qx PROPN hjic-1073 18 3 + + ADJ hjic-1073 18 4 xf+g::o xf+g::o PROPN hjic-1073 18 5 ( ( PUNCT hjic-1073 18 6 4 4 NUM hjic-1073 18 7 ) ) PUNCT hjic-1073 18 8 a a DET hjic-1073 18 9 linear linear ADJ hjic-1073 18 10 matrix matrix NOUN hjic-1073 18 11 equation equation NOUN hjic-1073 18 12 , , PUNCT hjic-1073 18 13 solutions solution NOUN hjic-1073 18 14 xi xi X hjic-1073 18 15 of of ADP hjic-1073 18 16 which which PRON hjic-1073 18 17 converge converge VERB hjic-1073 18 18 to to ADP hjic-1073 18 19 x x PROPN hjic-1073 18 20 the the DET hjic-1073 18 21 solution solution NOUN hjic-1073 18 22 of of ADP hjic-1073 18 23 eqn eqn PROPN hjic-1073 18 24 . . PUNCT hjic-1073 19 1 ( ( PUNCT hjic-1073 19 2 4 4 NUM hjic-1073 19 3 ) ) PUNCT hjic-1073 19 4 under under ADP hjic-1073 19 5 appropriate appropriate ADJ hjic-1073 19 6 conditions condition NOUN hjic-1073 19 7 , , PUNCT hjic-1073 19 8 is be AUX hjic-1073 19 9 obtained obtain VERB hjic-1073 19 10 . . PUNCT hjic-1073 20 1 there there PRON hjic-1073 20 2 are be VERB hjic-1073 20 3 many many ADJ hjic-1073 20 4 possible possible ADJ hjic-1073 20 5 ways way NOUN hjic-1073 20 6 of of ADP hjic-1073 20 7 solving solve VERB hjic-1073 20 8 this this DET hjic-1073 20 9 linear linear ADJ hjic-1073 20 10 matrix matrix NOUN hjic-1073 20 11 equation equation NOUN hjic-1073 20 12 ( ( PUNCT hjic-1073 20 13 see see VERB hjic-1073 20 14 , , PUNCT hjic-1073 20 15 e.g. e.g. ADV hjic-1073 20 16 , , PUNCT hjic-1073 20 17 ( ( PUNCT hjic-1073 20 18 5 5 NUM hjic-1073 20 19 ] ] PUNCT hjic-1073 20 20 ) ) PUNCT hjic-1073 20 21 and and CCONJ hjic-1073 20 22 one one NUM hjic-1073 20 23 of of ADP hjic-1073 20 24 these these PRON hjic-1073 20 25 , , PUNCT hjic-1073 20 26 which which PRON hjic-1073 20 27 involves involve VERB hjic-1073 20 28 infmite infmite ADJ hjic-1073 20 29 series series NOUN hjic-1073 20 30 , , PUNCT hjic-1073 20 31 is be AUX hjic-1073 20 32 studied study VERB hjic-1073 20 33 in in ADP hjic-1073 20 34 { { PUNCT hjic-1073 20 35 6 6 NUM hjic-1073 20 36 ] ] PUNCT hjic-1073 20 37 . . PUNCT hjic-1073 21 1 methods method NOUN hjic-1073 21 2 for for ADP hjic-1073 21 3 offsetting offset VERB hjic-1073 21 4 the the DET hjic-1073 21 5 difficulties difficulty NOUN hjic-1073 21 6 involved involve VERB hjic-1073 21 7 if if SCONJ hjic-1073 21 8 a a DET hjic-1073 21 9 poor poor ADJ hjic-1073 21 10 starting starting NOUN hjic-1073 21 11 approximation approximation NOUN hjic-1073 21 12 is be AUX hjic-1073 21 13 made make VERB hjic-1073 21 14 to to ADP hjic-1073 21 15 the the DET hjic-1073 21 16 solution solution NOUN hjic-1073 21 17 and and CCONJ hjic-1073 21 18 for for ADP hjic-1073 21 19 accelerating accelerate VERB hjic-1073 21 20 convergence convergence NOUN hjic-1073 21 21 are be AUX hjic-1073 21 22 also also ADV hjic-1073 21 23 investigated investigate VERB hjic-1073 21 24 in in ADP hjic-1073 21 25 [ [ X hjic-1073 21 26 6 6 NUM hjic-1073 21 27 } } PUNCT hjic-1073 21 28 . . PUNCT hjic-1073 22 1 the the DET hjic-1073 22 2 solution solution NOUN hjic-1073 22 3 techniques technique NOUN hjic-1073 22 4 are be AUX hjic-1073 22 5 implemented implement VERB hjic-1073 22 6 by by ADP hjic-1073 22 7 two two NUM hjic-1073 22 8 algorithms algorithm NOUN hjic-1073 22 9 , , PUNCT hjic-1073 22 10 ai ai VERB hjic-1073 22 11 and and CCONJ hjic-1073 22 12 a2 a2 PROPN hjic-1073 22 13 , , PUNCT hjic-1073 22 14 depending depend VERB hjic-1073 22 15 on on ADP hjic-1073 22 16 whether whether SCONJ hjic-1073 22 17 x x PRON hjic-1073 22 18 is be AUX hjic-1073 22 19 unsymmetric unsymmetric ADJ hjic-1073 22 20 or or CCONJ hjic-1073 22 21 symmetric symmetric ADJ hjic-1073 22 22 . . PUNCT hjic-1073 23 1 a a DET hjic-1073 23 2 simplified simplified ADJ hjic-1073 23 3 form form NOUN hjic-1073 23 4 of of ADP hjic-1073 23 5 al al PROPN hjic-1073 23 6 is be AUX hjic-1073 23 7 given give VERB hjic-1073 23 8 in in ADP hjic-1073 23 9 the the DET hjic-1073 23 10 appendix appendix NOUN hjic-1073 23 11 for for ADP hjic-1073 23 12 convenience convenience NOUN hjic-1073 23 13 . . PUNCT hjic-1073 24 1 the the DET hjic-1073 24 2 aim aim NOUN hjic-1073 24 3 of of ADP hjic-1073 24 4 the the DET hjic-1073 24 5 present present ADJ hjic-1073 24 6 paper paper NOUN hjic-1073 24 7 is be AUX hjic-1073 24 8 to to PART hjic-1073 24 9 illustrate illustrate VERB hjic-1073 24 10 the the DET hjic-1073 24 11 use use NOUN hjic-1073 24 12 of of ADP hjic-1073 24 13 ai ai NOUN hjic-1073 24 14 in in ADP hjic-1073 24 15 solving solve VERB hjic-1073 24 16 ls ls ADJ hjic-1073 24 17 and and CCONJ hjic-1073 24 18 tls tls PROPN hjic-1073 24 19 problems problem NOUN hjic-1073 24 20 by by ADP hjic-1073 24 21 means mean NOUN hjic-1073 24 22 of of ADP hjic-1073 24 23 a a DET hjic-1073 24 24 number number NOUN hjic-1073 24 25 of of ADP hjic-1073 24 26 numerical numerical ADJ hjic-1073 24 27 examples example NOUN hjic-1073 24 28 from from ADP hjic-1073 24 29 the the DET hjic-1073 24 30 literature literature NOUN hjic-1073 24 31 . . PUNCT hjic-1073 25 1 numerical numerical PROPN hjic-1073 25 2 results results PROPN hjic-1073 25 3 example example VERB hjic-1073 25 4 1 1 NUM hjic-1073 25 5 the the DET hjic-1073 25 6 first first ADJ hjic-1073 25 7 example example NOUN hjic-1073 25 8 is be AUX hjic-1073 25 9 taken take VERB hjic-1073 25 10 from from ADP hjic-1073 25 11 [ [ X hjic-1073 25 12 7 7 NUM hjic-1073 25 13 ] ] PUNCT hjic-1073 25 14 and and CCONJ hjic-1073 25 15 is be AUX hjic-1073 25 16 concerned concern VERB hjic-1073 25 17 with with ADP hjic-1073 25 18 modelling model VERB hjic-1073 25 19 the the DET hjic-1073 25 20 biological biological ADJ hjic-1073 25 21 activity activity NOUN hjic-1073 25 22 of of ADP hjic-1073 25 23 fifteen fifteen NUM hjic-1073 25 24 different different ADJ hjic-1073 25 25 compounds compound NOUN hjic-1073 25 26 with with ADP hjic-1073 25 27 respect respect NOUN hjic-1073 25 28 to to ADP hjic-1073 25 29 a a DET hjic-1073 25 30 set set NOUN hjic-1073 25 31 of of ADP hjic-1073 25 32 eight eight NUM hjic-1073 25 33 variables variable NOUN hjic-1073 25 34 which which PRON hjic-1073 25 35 describe describe VERB hjic-1073 25 36 the the DET hjic-1073 25 37 various various ADJ hjic-1073 25 38 morphological morphological ADJ hjic-1073 25 39 and and CCONJ hjic-1073 25 40 physiochemical physiochemical ADJ hjic-1073 25 41 properties property NOUN hjic-1073 25 42 of of ADP hjic-1073 25 43 the the DET hjic-1073 25 44 compounds compound NOUN hjic-1073 25 45 . . PUNCT hjic-1073 26 1 the the DET hjic-1073 26 2 data datum NOUN hjic-1073 26 3 used use VERB hjic-1073 26 4 is be AUX hjic-1073 26 5 given give VERB hjic-1073 26 6 in in ADP hjic-1073 26 7 table table NOUN hjic-1073 26 8 1 1 NUM hjic-1073 26 9 of of ADP hjic-1073 26 10 { { PUNCT hjic-1073 26 11 7 7 NUM hjic-1073 26 12 ] ] PUNCT hjic-1073 26 13 . . PUNCT hjic-1073 27 1 setting set VERB hjic-1073 27 2 the the DET hjic-1073 27 3 initial initial ADJ hjic-1073 27 4 approximation approximation NOUN hjic-1073 27 5 x0 x0 PROPN hjic-1073 28 1 = = NOUN hjic-1073 28 2 0 0 PROPN hjic-1073 28 3 in in ADP hjic-1073 28 4 al al PROPN hjic-1073 28 5 gave give VERB hjic-1073 28 6 the the DET hjic-1073 28 7 same same ADJ hjic-1073 28 8 least least ADJ hjic-1073 28 9 squares square NOUN hjic-1073 28 10 solution solution NOUN hjic-1073 28 11 as as ADP hjic-1073 28 12 in in ADP hjic-1073 28 13 17 17 NUM hjic-1073 28 14 ] ] PUNCT hjic-1073 28 15 ( ( PUNCT hjic-1073 28 16 when when SCONJ hjic-1073 28 17 rounded rounded ADJ hjic-1073 28 18 ) ) PUNCT hjic-1073 28 19 . . PUNCT hjic-1073 29 1 68 68 NUM hjic-1073 29 2 xls xls NOUN hjic-1073 29 3 = = PUNCT hjic-1073 30 1 [ [ X hjic-1073 30 2 0.636 0.636 NUM hjic-1073 30 3 , , PUNCT hjic-1073 30 4 0.080 0.080 NUM hjic-1073 30 5 , , PUNCT hjic-1073 30 6 0.095 0.095 NUM hjic-1073 30 7 , , PUNCT hjic-1073 30 8 -0.308 -0.308 PRON hjic-1073 30 9 , , PUNCT hjic-1073 30 10 0.169 0.169 NUM hjic-1073 30 11 , , PUNCT hjic-1073 30 12 0.241 0.241 NUM hjic-1073 30 13 , , PUNCT hjic-1073 30 14 0.278 0.278 NUM hjic-1073 30 15 , , PUNCT hjic-1073 30 16 0.238f 0.238f NOUN hjic-1073 30 17 and and CCONJ hjic-1073 30 18 , , PUNCT hjic-1073 30 19 of of ADP hjic-1073 30 20 course course NOUN hjic-1073 30 21 , , PUNCT hjic-1073 30 22 the the DET hjic-1073 30 23 same same ADJ hjic-1073 30 24 value value NOUN hjic-1073 30 25 , , PUNCT hjic-1073 30 26 0.61 0.61 NUM hjic-1073 30 27 , , PUNCT hjic-1073 30 28 for for ADP hjic-1073 30 29 the the DET hjic-1073 30 30 residual residual ADJ hjic-1073 30 31 sum sum NOUN hjic-1073 30 32 of of ADP hjic-1073 30 33 squares square NOUN hjic-1073 30 34 ss ss PROPN hjic-1073 30 35 . . PUNCT hjic-1073 31 1 x x PROPN hjic-1073 31 2 ls ls PROPN hjic-1073 31 3 also also ADV hjic-1073 31 4 agrees agree VERB hjic-1073 31 5 with with ADP hjic-1073 31 6 l+ l+ NOUN hjic-1073 31 7 m m VERB hjic-1073 31 8 where where SCONJ hjic-1073 31 9 l+ l+ PUNCT hjic-1073 31 10 is be AUX hjic-1073 31 11 the the DET hjic-1073 31 12 pseudo pseudo NOUN hjic-1073 31 13 - - NOUN hjic-1073 31 14 inverse inverse NOUN hjic-1073 31 15 of of ADP hjic-1073 31 16 l. l. PROPN hjic-1073 31 17 the the DET hjic-1073 31 18 smallest small ADJ hjic-1073 31 19 singular singular ADJ hjic-1073 31 20 value value NOUN hjic-1073 31 21 of of ADP hjic-1073 31 22 lis li NOUN hjic-1073 31 23 0.337365 0.337365 NUM hjic-1073 31 24 and and CCONJ hjic-1073 31 25 of of ADP hjic-1073 31 26 [ [ X hjic-1073 31 27 l;m l;m X hjic-1073 31 28 ] ] X hjic-1073 31 29 is be AUX hjic-1073 31 30 0.335713 0.335713 NUM hjic-1073 31 31 so so SCONJ hjic-1073 31 32 that that SCONJ hjic-1073 31 33 conditions condition NOUN hjic-1073 31 34 for for ADP hjic-1073 31 35 a a DET hjic-1073 31 36 unique unique ADJ hjic-1073 31 37 tls tls NOUN hjic-1073 31 38 solution solution NOUN hjic-1073 31 39 , , PUNCT hjic-1073 31 40 [ [ X hjic-1073 31 41 2 2 NUM hjic-1073 31 42 ] ] PUNCT hjic-1073 31 43 , , PUNCT hjic-1073 31 44 are be AUX hjic-1073 31 45 gust gust NOUN hjic-1073 31 46 ) ) PUNCT hjic-1073 31 47 satisfied satisfied ADJ hjic-1073 31 48 . . PUNCT hjic-1073 32 1 if if SCONJ hjic-1073 32 2 a1 a1 NOUN hjic-1073 32 3 is be AUX hjic-1073 32 4 now now ADV hjic-1073 32 5 continued continue VERB hjic-1073 32 6 from from ADP hjic-1073 32 7 the the DET hjic-1073 32 8 solution solution NOUN hjic-1073 32 9 x x PUNCT hjic-1073 32 10 ls ls ADJ hjic-1073 32 11 given give VERB hjic-1073 32 12 above above ADP hjic-1073 32 13 it it PRON hjic-1073 32 14 converges converge VERB hjic-1073 32 15 to to ADP hjic-1073 32 16 x= x= PROPN hjic-1073 33 1 [ [ X hjic-1073 33 2 0.716 0.716 NUM hjic-1073 33 3 , , PUNCT hjic-1073 33 4 0.259 0.259 NUM hjic-1073 33 5 , , PUNCT hjic-1073 33 6 0.124 0.124 NUM hjic-1073 33 7 , , PUNCT hjic-1073 33 8 -0.336 -0.336 NOUN hjic-1073 33 9 , , PUNCT hjic-1073 33 10 0.186 0.186 NUM hjic-1073 33 11 , , PUNCT hjic-1073 33 12 0.531 0.531 NUM hjic-1073 33 13 , , PUNCT hjic-1073 33 14 -0.435 -0.435 NOUN hjic-1073 33 15 , , PUNCT hjic-1073 33 16 0.337f 0.337f NOUN hjic-1073 33 17 with with ADP hjic-1073 33 18 e e PROPN hjic-1073 33 19 = = SYM hjic-1073 33 20 0.16 0.16 NUM hjic-1073 33 21 before before SCONJ hjic-1073 33 22 accuracy accuracy NOUN hjic-1073 33 23 begins begin VERB hjic-1073 33 24 to to PART hjic-1073 33 25 deteriorate deteriorate VERB hjic-1073 33 26 . . PUNCT hjic-1073 34 1 ( ( PUNCT hjic-1073 34 2 using use VERB hjic-1073 34 3 a a DET hjic-1073 34 4 line line NOUN hjic-1073 34 5 search search NOUN hjic-1073 34 6 shows show VERB hjic-1073 34 7 a a DET hjic-1073 34 8 slight slight ADJ hjic-1073 34 9 improvement improvement NOUN hjic-1073 34 10 in in ADP hjic-1073 34 11 accuracy accuracy NOUN hjic-1073 34 12 before before ADP hjic-1073 34 13 deterioration deterioration NOUN hjic-1073 34 14 . . PUNCT hjic-1073 34 15 ) ) PUNCT hjic-1073 35 1 when when SCONJ hjic-1073 35 2 this this DET hjic-1073 35 3 model model NOUN hjic-1073 35 4 is be AUX hjic-1073 35 5 applied apply VERB hjic-1073 35 6 to to ADP hjic-1073 35 7 the the DET hjic-1073 35 8 whole whole NOUN hjic-1073 35 9 of of ADP hjic-1073 35 10 the the DET hjic-1073 35 11 data datum NOUN hjic-1073 35 12 the the DET hjic-1073 35 13 resulting result VERB hjic-1073 35 14 sum sum NOUN hjic-1073 35 15 of of ADP hjic-1073 35 16 squares square NOUN hjic-1073 35 17 is be AUX hjic-1073 35 18 41.893 41.893 NUM hjic-1073 35 19 . . PUNCT hjic-1073 36 1 , , PUNCT hjic-1073 36 2 the the DET hjic-1073 36 3 smallest small ADJ hjic-1073 36 4 singular singular ADJ hjic-1073 36 5 value value NOUN hjic-1073 36 6 of of ADP hjic-1073 36 7 [ [ X hjic-1073 36 8 l;m l;m X hjic-1073 36 9 ] ] X hjic-1073 36 10 , , PUNCT hjic-1073 36 11 for for ADP hjic-1073 36 12 this this DET hjic-1073 36 13 example example NOUN hjic-1073 36 14 , , PUNCT hjic-1073 36 15 is be AUX hjic-1073 36 16 as as SCONJ hjic-1073 36 17 given give VERB hjic-1073 36 18 above above ADV hjic-1073 36 19 and and CCONJ hjic-1073 36 20 the the DET hjic-1073 36 21 svd svd PROPN hjic-1073 36 22 formula formula VERB hjic-1073 36 23 x= x= PUNCT hjic-1073 37 1 [ [ X hjic-1073 37 2 l:.l-(0.335713)2 l:.l-(0.335713)2 PROPN hjic-1073 37 3 13j1 13j1 NUM hjic-1073 37 4 ltm ltm PROPN hjic-1073 37 5 gives give VERB hjic-1073 37 6 x x PUNCT hjic-1073 37 7 = = PUNCT hjic-1073 37 8 [ [ PUNCT hjic-1073 37 9 -4.28 -4.28 NOUN hjic-1073 37 10 , , PUNCT hjic-1073 37 11 . . PUNCT hjic-1073 38 1 1.20,2.21 1.20,2.21 NUM hjic-1073 38 2 , , PUNCT hjic-1073 38 3 -1.29 -1.29 PROPN hjic-1073 38 4 , , PUNCT hjic-1073 38 5 2.36 2.36 NUM hjic-1073 38 6 , , PUNCT hjic-1073 38 7 11.oo 11.oo NUM hjic-1073 38 8 , , PUNCT hjic-1073 38 9 -14.60 -14.60 PROPN hjic-1073 38 10 , , PUNCT hjic-1073 38 11 2.1ot 2.1ot NUM hjic-1073 38 12 which which PRON hjic-1073 38 13 has have VERB hjic-1073 38 14 a a DET hjic-1073 38 15 residual residual ADJ hjic-1073 38 16 error error NOUN hjic-1073 38 17 e e NOUN hjic-1073 38 18 = = SYM hjic-1073 38 19 6 6 NUM hjic-1073 38 20 ( ( PUNCT hjic-1073 38 21 -4 -4 INTJ hjic-1073 38 22 ) ) PUNCT hjic-1073 38 23 and and CCONJ hjic-1073 38 24 which which PRON hjic-1073 38 25 is be AUX hjic-1073 38 26 much much ADV hjic-1073 38 27 better well ADJ hjic-1073 38 28 than than ADP hjic-1073 38 29 the the DET hjic-1073 38 30 previous previous ADJ hjic-1073 38 31 result result NOUN hjic-1073 38 32 from from ADP hjic-1073 38 33 al al PROPN hjic-1073 38 34 . . PUNCT hjic-1073 39 1 if if SCONJ hjic-1073 39 2 now now ADV hjic-1073 39 3 , , PUNCT hjic-1073 39 4 however however ADV hjic-1073 39 5 , , PUNCT hjic-1073 39 6 the the DET hjic-1073 39 7 above above ADJ hjic-1073 39 8 x x AUX hjic-1073 39 9 is be AUX hjic-1073 39 10 used use VERB hjic-1073 39 11 as as ADP hjic-1073 39 12 the the DET hjic-1073 39 13 starting start VERB hjic-1073 39 14 approx.imation approx.imation NOUN hjic-1073 39 15 in in ADP hjic-1073 39 16 a1 a1 NOUN hjic-1073 39 17 the the DET hjic-1073 39 18 result result NOUN hjic-1073 39 19 is be AUX hjic-1073 39 20 refined refine VERB hjic-1073 39 21 to to PART hjic-1073 39 22 give give VERB hjic-1073 39 23 a a DET hjic-1073 39 24 better well ADJ hjic-1073 39 25 x x NOUN hjic-1073 39 26 with with ADP hjic-1073 39 27 a a DET hjic-1073 39 28 residual residual ADJ hjic-1073 39 29 error error NOUN hjic-1073 39 30 less less ADJ hjic-1073 39 31 than than ADP hjic-1073 39 32 10(-6 10(-6 NUM hjic-1073 39 33 ) ) PUNCT hjic-1073 39 34 . . PUNCT hjic-1073 40 1 algorithm algorithm PROPN hjic-1073 40 2 al al PROPN hjic-1073 40 3 was be AUX hjic-1073 40 4 also also ADV hjic-1073 40 5 used use VERB hjic-1073 40 6 to to PART hjic-1073 40 7 compute compute VERB hjic-1073 40 8 the the DET hjic-1073 40 9 sums sum NOUN hjic-1073 40 10 of of ADP hjic-1073 40 11 squares square NOUN hjic-1073 40 12 , , PUNCT hjic-1073 40 13 denoted denote VERB hjic-1073 40 14 by by ADP hjic-1073 40 15 '' '' PUNCT hjic-1073 40 16 press press NOUN hjic-1073 40 17 " " PUNCT hjic-1073 40 18 in in ADP hjic-1073 40 19 [ [ X hjic-1073 40 20 7 7 NUM hjic-1073 40 21 ] ] PUNCT hjic-1073 40 22 , , PUNCT hjic-1073 40 23 for for ADP hjic-1073 40 24 both both CCONJ hjic-1073 40 25 ls ls ADJ hjic-1073 40 26 and and CCONJ hjic-1073 40 27 tls tls PROPN hjic-1073 40 28 ; ; PUNCT hjic-1073 40 29 these these PRON hjic-1073 40 30 measure measure VERB hjic-1073 40 31 the the DET hjic-1073 40 32 predictive predictive ADJ hjic-1073 40 33 properties property NOUN hjic-1073 40 34 of of ADP hjic-1073 40 35 the the DET hjic-1073 40 36 models model NOUN hjic-1073 40 37 used use VERB hjic-1073 40 38 . . PUNCT hjic-1073 41 1 the the DET hjic-1073 41 2 same same ADJ hjic-1073 41 3 groupings grouping NOUN hjic-1073 41 4 of of ADP hjic-1073 41 5 the the DET hjic-1073 41 6 date date NOUN hjic-1073 41 7 were be AUX hjic-1073 41 8 used use VERB hjic-1073 41 9 as as ADP hjic-1073 41 10 in in ADP hjic-1073 41 11 [ [ X hjic-1073 41 12 7 7 NUM hjic-1073 41 13 ] ] PUNCT hjic-1073 41 14 and and CCONJ hjic-1073 41 15 table table NOUN hjic-1073 41 16 1 1 NUM hjic-1073 41 17 shows show VERB hjic-1073 41 18 the the DET hjic-1073 41 19 results result NOUN hjic-1073 41 20 obtained obtain VERB hjic-1073 41 21 . . PUNCT hjic-1073 42 1 table table NOUN hjic-1073 42 2 1 1 NUM hjic-1073 42 3 predictive predictive ADJ hjic-1073 42 4 sums sum NOUN hjic-1073 42 5 of of ADP hjic-1073 42 6 squares square NOUN hjic-1073 42 7 for for ADP hjic-1073 42 8 example example NOUN hjic-1073 42 9 1 1 NUM hjic-1073 42 10 ls ls PROPN hjic-1073 42 11 tls tls PROPN hjic-1073 42 12 group group NOUN hjic-1073 42 13 1 1 NUM hjic-1073 42 14 1.172 1.172 NUM hjic-1073 42 15 1.319 1.319 NUM hjic-1073 42 16 group group NOUN hjic-1073 42 17 2 2 NUM hjic-1073 42 18 group group NOUN hjic-1073 42 19 3 3 NUM hjic-1073 42 20 total total NOUN hjic-1073 42 21 1.183 1.183 NUM hjic-1073 42 22 0.804 0.804 NUM hjic-1073 42 23 3.159 3.159 NUM hjic-1073 42 24 1.540 1.540 NUM hjic-1073 42 25 34.832 34.832 NUM hjic-1073 42 26 37.691 37.691 NUM hjic-1073 42 27 the the DET hjic-1073 42 28 total total NOUN hjic-1073 42 29 for for ADP hjic-1073 42 30 ls ls PROPN hjic-1073 42 31 agrees agree VERB hjic-1073 42 32 with with ADP hjic-1073 42 33 that that PRON hjic-1073 42 34 given give VERB hjic-1073 42 35 in in ADP hjic-1073 42 36 [ [ X hjic-1073 42 37 7 7 NUM hjic-1073 42 38 ] ] PUNCT hjic-1073 42 39 . . PUNCT hjic-1073 43 1 the the DET hjic-1073 43 2 total total NOUN hjic-1073 43 3 for for ADP hjic-1073 43 4 tls tls PROPN hjic-1073 43 5 is be AUX hjic-1073 43 6 inflated inflate VERB hjic-1073 43 7 by by ADP hjic-1073 43 8 the the DET hjic-1073 43 9 very very ADV hjic-1073 43 10 large large ADJ hjic-1073 43 11 value value NOUN hjic-1073 43 12 from from ADP hjic-1073 43 13 group group NOUN hjic-1073 43 14 3 3 NUM hjic-1073 43 15 and and CCONJ hjic-1073 43 16 presumably presumably ADV hjic-1073 43 17 accounts account VERB hjic-1073 43 18 for for ADP hjic-1073 43 19 the the DET hjic-1073 43 20 comment comment NOUN hjic-1073 43 21 , , PUNCT hjic-1073 43 22 .. .. PUNCT hjic-1073 43 23 when when SCONJ hjic-1073 43 24 full full ADJ hjic-1073 43 25 rank rank NOUN hjic-1073 43 26 is be AUX hjic-1073 43 27 approached approach VERB hjic-1073 43 28 , , PUNCT hjic-1073 43 29 it it PRON hjic-1073 43 30 behaved behave VERB hjic-1073 43 31 differently differently ADV hjic-1073 43 32 , , PUNCT hjic-1073 43 33 " " PUNCT hjic-1073 43 34 made make VERB hjic-1073 43 35 regarding regard VERB hjic-1073 43 36 tls tls NOUN hjic-1073 43 37 in in ADP hjic-1073 43 38 [ [ X hjic-1073 43 39 7 7 NUM hjic-1073 43 40 ] ] PUNCT hjic-1073 43 41 and and CCONJ hjic-1073 43 42 for for ADP hjic-1073 43 43 the the DET hjic-1073 43 44 use use NOUN hjic-1073 43 45 of of ADP hjic-1073 43 46 rank rank PROPN hjic-1073 43 47 3 3 NUM hjic-1073 43 48 tls tls PROPN hjic-1073 43 49 rather rather ADV hjic-1073 43 50 than than ADP hjic-1073 43 51 full full ADJ hjic-1073 43 52 rank rank NOUN hjic-1073 43 53 . . PUNCT hjic-1073 44 1 ( ( PUNCT hjic-1073 44 2 before before ADP hjic-1073 44 3 making make VERB hjic-1073 44 4 the the DET hjic-1073 44 5 calculations calculation NOUN hjic-1073 44 6 all all DET hjic-1073 44 7 the the DET hjic-1073 44 8 nine nine NUM hjic-1073 44 9 sets set NOUN hjic-1073 44 10 of of ADP hjic-1073 44 11 data datum NOUN hjic-1073 44 12 were be AUX hjic-1073 44 13 scaled scale VERB hjic-1073 44 14 to to PART hjic-1073 44 15 have have VERB hjic-1073 44 16 zero zero NUM hjic-1073 44 17 mean mean NOUN hjic-1073 44 18 and and CCONJ hjic-1073 44 19 unit unit NOUN hjic-1073 44 20 variance variance NOUN hjic-1073 44 21 . . PUNCT hjic-1073 44 22 ) ) PUNCT hjic-1073 45 1 example2 example2 PROPN hjic-1073 46 1 this this DET hjic-1073 46 2 example example NOUN hjic-1073 46 3 is be AUX hjic-1073 46 4 taken take VERB hjic-1073 46 5 from from ADP hjic-1073 46 6 { { PUNCT hjic-1073 46 7 l l NOUN hjic-1073 46 8 ] ] PUNCT hjic-1073 46 9 and and CCONJ hjic-1073 46 10 involves involve VERB hjic-1073 46 11 finding find VERB hjic-1073 46 12 a a DET hjic-1073 46 13 linear linear ADJ hjic-1073 46 14 fit fit NOUN hjic-1073 46 15 to to ADP hjic-1073 46 16 data datum NOUN hjic-1073 46 17 given give VERB hjic-1073 46 18 in in ADP hjic-1073 46 19 table table NOUN hjic-1073 46 20 26.1 26.1 NUM hjic-1073 46 21 in in ADP hjic-1073 46 22 that that DET hjic-1073 46 23 reference reference NOUN hjic-1073 46 24 . . PUNCT hjic-1073 47 1 in in SCONJ hjic-1073 47 2 ( ( PUNCT hjic-1073 47 3 11 11 NUM hjic-1073 47 4 five five NUM hjic-1073 47 5 different different ADJ hjic-1073 47 6 ucandidaten ucandidaten NOUN hjic-1073 47 7 solutions solution NOUN hjic-1073 47 8 are be AUX hjic-1073 47 9 obtained obtain VERB hjic-1073 47 10 and and CCONJ hjic-1073 47 11 one one NUM hjic-1073 47 12 of of ADP hjic-1073 47 13 them they PRON hjic-1073 47 14 x x PUNCT hjic-1073 48 1 = = PROPN hjic-1073 48 2 f-2.486~-q.529.-0.l94.1.616,3.455 f-2.486~-q.529.-0.l94.1.616,3.455 PROPN hjic-1073 48 3 t t PROPN hjic-1073 48 4 ( ( PUNCT hjic-1073 48 5 5 5 NUM hjic-1073 48 6 ) ) PUNCT hjic-1073 48 7 is be AUX hjic-1073 48 8 proposed propose VERB hjic-1073 48 9 as as ADP hjic-1073 48 10 the the DET hjic-1073 48 11 best good ADJ hjic-1073 48 12 ls ls ADJ hjic-1073 48 13 solution solution NOUN hjic-1073 48 14 according accord VERB hjic-1073 48 15 to to ADP hjic-1073 48 16 a a DET hjic-1073 48 17 number number NOUN hjic-1073 48 18 of of ADP hjic-1073 48 19 statistical statistical ADJ hjic-1073 48 20 criteria criterion NOUN hjic-1073 48 21 . . PUNCT hjic-1073 49 1 now now ADV hjic-1073 49 2 if if SCONJ hjic-1073 49 3 a1 a1 NOUN hjic-1073 49 4 is be AUX hjic-1073 49 5 used use VERB hjic-1073 49 6 to to PART hjic-1073 49 7 find find VERB hjic-1073 49 8 a a DET hjic-1073 49 9 ls ls NOUN hjic-1073 49 10 and and CCONJ hjic-1073 49 11 then then ADV hjic-1073 49 12 a a DET hjic-1073 49 13 tsl tsl PROPN hjic-1073 49 14 solution solution NOUN hjic-1073 49 15 the the DET hjic-1073 49 16 result result NOUN hjic-1073 49 17 is be AUX hjic-1073 49 18 x x X hjic-1073 49 19 = = PUNCT hjic-1073 49 20 [ [ PUNCT hjic-1073 49 21 -73.3 -73.3 X hjic-1073 49 22 , , PUNCT hjic-1073 49 23 98.4 98.4 NUM hjic-1073 49 24 , , PUNCT hjic-1073 49 25 -78.0 -78.0 INTJ hjic-1073 49 26 , , PUNCT hjic-1073 49 27 90.7,78.2f 90.7,78.2f NUM hjic-1073 49 28 ( ( PUNCT hjic-1073 49 29 6 6 NUM hjic-1073 49 30 ) ) PUNCT hjic-1073 49 31 which which PRON hjic-1073 49 32 is be AUX hjic-1073 49 33 very very ADV hjic-1073 49 34 different different ADJ hjic-1073 49 35 from from ADP hjic-1073 49 36 the the DET hjic-1073 49 37 solution solution NOUN hjic-1073 49 38 given give VERB hjic-1073 49 39 in in ADP hjic-1073 49 40 eqn eqn NOUN hjic-1073 49 41 . . PUNCT hjic-1073 50 1 ( ( PUNCT hjic-1073 50 2 5 5 NUM hjic-1073 50 3 ) ) PUNCT hjic-1073 50 4 despite despite SCONJ hjic-1073 50 5 the the DET hjic-1073 50 6 fact fact NOUN hjic-1073 50 7 that that SCONJ hjic-1073 50 8 their their PRON hjic-1073 50 9 residual residual ADJ hjic-1073 50 10 norms norm NOUN hjic-1073 50 11 are be AUX hjic-1073 50 12 quite quite ADV hjic-1073 50 13 close close ADJ hjic-1073 50 14 . . PUNCT hjic-1073 51 1 it it PRON hjic-1073 51 2 is be AUX hjic-1073 51 3 also also ADV hjic-1073 51 4 interesting interesting ADJ hjic-1073 51 5 that that SCONJ hjic-1073 51 6 the the DET hjic-1073 51 7 norm norm NOUN hjic-1073 51 8 of of ADP hjic-1073 51 9 ( ( PUNCT hjic-1073 51 10 5 5 NUM hjic-1073 51 11 ) ) PUNCT hjic-1073 51 12 is be AUX hjic-1073 51 13 only only ADV hjic-1073 51 14 about about ADV hjic-1073 51 15 4.6 4.6 NUM hjic-1073 51 16 compared compare VERB hjic-1073 51 17 with with ADP hjic-1073 51 18 188 188 NUM hjic-1073 51 19 for for ADP hjic-1073 51 20 that that PRON hjic-1073 51 21 of of ADP hjic-1073 51 22 ( ( PUNCT hjic-1073 51 23 6 6 NUM hjic-1073 51 24 ) ) PUNCT hjic-1073 51 25 and and CCONJ hjic-1073 51 26 that that SCONJ hjic-1073 51 27 the the DET hjic-1073 51 28 smallness smallness NOUN hjic-1073 51 29 of of ADP hjic-1073 51 30 norm norm NOUN hjic-1073 51 31 is be AUX hjic-1073 51 32 one one NUM hjic-1073 51 33 of of ADP hjic-1073 51 34 the the DET hjic-1073 51 35 criteria criterion NOUN hjic-1073 51 36 mentioned mention VERB hjic-1073 51 37 above above ADV hjic-1073 51 38 for for ADP hjic-1073 51 39 preferring prefer VERB hjic-1073 51 40 one one NUM hjic-1073 51 41 solution solution NOUN hjic-1073 51 42 to to ADP hjic-1073 51 43 another another PRON hjic-1073 51 44 . . PUNCT hjic-1073 52 1 the the DET hjic-1073 52 2 tsl tsl PROPN hjic-1073 52 3 solution solution NOUN hjic-1073 52 4 would would AUX hjic-1073 52 5 not not PART hjic-1073 52 6 have have AUX hjic-1073 52 7 found find VERB hjic-1073 52 8 much much ADJ hjic-1073 52 9 favour favour NOUN hjic-1073 52 10 from from ADP hjic-1073 52 11 this this DET hjic-1073 52 12 particular particular ADJ hjic-1073 52 13 viewpoint viewpoint NOUN hjic-1073 52 14 . . PUNCT hjic-1073 53 1 example example NOUN hjic-1073 53 2 3 3 NUM hjic-1073 53 3 this this DET hjic-1073 53 4 example example NOUN hjic-1073 53 5 , , PUNCT hjic-1073 53 6 with with ADP hjic-1073 53 7 l=(~~ l=(~~ NOUN hjic-1073 53 8 ) ) PUNCT hjic-1073 53 9 and and CCONJ hjic-1073 53 10 m m PROPN hjic-1073 53 11 = = NOUN hjic-1073 53 12 g g NOUN hjic-1073 53 13 ) ) PUNCT hjic-1073 53 14 is be AUX hjic-1073 53 15 of of ADP hjic-1073 53 16 a a DET hjic-1073 53 17 type type NOUN hjic-1073 53 18 often often ADV hjic-1073 53 19 used use VERB hjic-1073 53 20 to to PART hjic-1073 53 21 show show VERB hjic-1073 53 22 that that SCONJ hjic-1073 53 23 the the DET hjic-1073 53 24 tsl tsl PROPN hjic-1073 53 25 problem problem NOUN hjic-1073 53 26 may may AUX hjic-1073 53 27 not not PART hjic-1073 53 28 have have VERB hjic-1073 53 29 a a DET hjic-1073 53 30 solution solution NOUN hjic-1073 53 31 unless unless SCONJ hjic-1073 53 32 extra extra ADJ hjic-1073 53 33 constraints constraint NOUN hjic-1073 53 34 are be AUX hjic-1073 53 35 imposed impose VERB hjic-1073 54 1 [ [ PUNCT hjic-1073 54 2 2 2 NUM hjic-1073 54 3 ] ] PUNCT hjic-1073 54 4 . . PUNCT hjic-1073 55 1 applying apply VERB hjic-1073 55 2 a1 a1 NOUN hjic-1073 55 3 , , PUNCT hjic-1073 55 4 using use VERB hjic-1073 55 5 x~ x~ NOUN hjic-1073 55 6 = = SYM hjic-1073 55 7 0 0 NUM hjic-1073 55 8 , , PUNCT hjic-1073 55 9 gives give VERB hjic-1073 55 10 the the DET hjic-1073 55 11 ls ls ADJ hjic-1073 55 12 solution solution NOUN hjic-1073 56 1 [ [ X hjic-1073 56 2 1,.0f 1,.0f NOUN hjic-1073 56 3 , , PUNCT hjic-1073 56 4 continuing continue VERB hjic-1073 56 5 until until SCONJ hjic-1073 56 6 convergence convergence NOUN hjic-1073 56 7 now now ADV hjic-1073 56 8 gives give VERB hjic-1073 56 9 the the DET hjic-1073 56 10 tsl tsl PROPN hjic-1073 56 11 solution solution NOUN hjic-1073 56 12 [ [ X hjic-1073 56 13 l61803,of l61803,of PROPN hjic-1073 56 14 . . PUNCT hjic-1073 57 1 another another DET hjic-1073 57 2 much much ADV hjic-1073 57 3 used use VERB hjic-1073 57 4 method method NOUN hjic-1073 57 5 for for ADP hjic-1073 57 6 solving solve VERB hjic-1073 57 7 problems problem NOUN hjic-1073 57 8 of of ADP hjic-1073 57 9 the the DET hjic-1073 57 10 kind kind NOUN hjic-1073 57 11 considered consider VERB hjic-1073 57 12 in in ADP hjic-1073 57 13 this this DET hjic-1073 57 14 paper paper NOUN hjic-1073 57 15 involves involve VERB hjic-1073 57 16 some some DET hjic-1073 57 17 form form NOUN hjic-1073 57 18 of of ADP hjic-1073 57 19 direct direct ADJ hjic-1073 57 20 minimization minimization NOUN hjic-1073 57 21 ( ( PUNCT hjic-1073 57 22 see see VERB hjic-1073 57 23 , , PUNCT hjic-1073 57 24 e.g. e.g. ADV hjic-1073 57 25 , , PUNCT hjic-1073 57 26 [ [ X hjic-1073 57 27 8 8 NUM hjic-1073 57 28 ] ] SYM hjic-1073 57 29 ) ) PUNCT hjic-1073 57 30 as as ADP hjic-1073 57 31 in in ADP hjic-1073 57 32 the the DET hjic-1073 57 33 following follow VERB hjic-1073 57 34 treatment treatment NOUN hjic-1073 57 35 . . PUNCT hjic-1073 58 1 let let VERB hjic-1073 58 2 ( ( PUNCT hjic-1073 58 3 xl xl PROPN hjic-1073 58 4 x2 x2 PROPN hjic-1073 58 5 ) ) PUNCT hjic-1073 58 6 , , PUNCT hjic-1073 58 7 ( ( PUNCT hjic-1073 58 8 xs xs PROPN hjic-1073 58 9 ) ) PUNCT hjic-1073 58 10 and and CCONJ hjic-1073 58 11 ( ( PUNCT hjic-1073 58 12 x7 x7 NOUN hjic-1073 58 13 ) ) PUNCT hjic-1073 58 14 x3 x3 PROPN hjic-1073 58 15 x4 x4 PROPN hjic-1073 58 16 x6 x6 PROPN hjic-1073 58 17 x8 x8 PROPN hjic-1073 58 18 be be VERB hjic-1073 58 19 estimates estimate NOUN hjic-1073 58 20 of of ADP hjic-1073 58 21 l l NOUN hjic-1073 58 22 , , PUNCT hjic-1073 58 23 x x PUNCT hjic-1073 58 24 and and CCONJ hjic-1073 58 25 m m PROPN hjic-1073 58 26 respectively respectively ADV hjic-1073 58 27 ; ; PUNCT hjic-1073 58 28 form form NOUN hjic-1073 58 29 + + CCONJ hjic-1073 58 30 ( ( PUNCT hjic-1073 58 31 1 1 NUM hjic-1073 58 32 \2 \2 SYM hjic-1073 58 33 2 2 NUM hjic-1073 58 34 2 2 NUM hjic-1073 58 35 2 2 NUM hjic-1073 58 36 j j NOUN hjic-1073 58 37 1 1 NUM hjic-1073 58 38 = = NOUN hjic-1073 58 39 -xi -xi PROPN hjic-1073 58 40 j j PROPN hjic-1073 59 1 + + CCONJ hjic-1073 59 2 x2 x2 PROPN hjic-1073 60 1 + + CCONJ hjic-1073 60 2 x3 x3 ADJ hjic-1073 60 3 + + CCONJ hjic-1073 60 4 x4 x4 PROPN hjic-1073 61 1 + + CCONJ hjic-1073 61 2 ( ( PUNCT hjic-1073 61 3 1 1 NUM hjic-1073 61 4 - - PUNCT hjic-1073 61 5 x1x5 x1x5 NOUN hjic-1073 61 6 -.xzx6 -.xzx6 NOUN hjic-1073 61 7 } } PUNCT hjic-1073 62 1 + + CCONJ hjic-1073 62 2 ( ( PUNCT hjic-1073 62 3 1x:3x5 1x:3x5 NUM hjic-1073 62 4 x4x6 x4x6 NUM hjic-1073 62 5 } } PUNCT hjic-1073 62 6 . . PUNCT hjic-1073 63 1 or or CCONJ hjic-1073 63 2 alternatively alternatively ADV hjic-1073 63 3 , , PUNCT hjic-1073 63 4 with with ADP hjic-1073 63 5 more more ADJ hjic-1073 63 6 variables variable NOUN hjic-1073 63 7 involved involve VERB hjic-1073 63 8 , , PUNCT hjic-1073 63 9 fz fz VERB hjic-1073 63 10 =( =( PROPN hjic-1073 63 11 1 1 PROPN hjic-1073 63 12 - - PUNCT hjic-1073 63 13 xl xl PROPN hjic-1073 63 14 } } PUNCT hjic-1073 63 15 + + PROPN hjic-1073 63 16 xz2 xz2 X hjic-1073 64 1 + + ADJ hjic-1073 64 2 x3 x3 ADJ hjic-1073 64 3 2 2 NUM hjic-1073 64 4 + + NOUN hjic-1073 64 5 x4 x4 PROPN hjic-1073 64 6 2 2 NUM hjic-1073 64 7 + + ADJ hjic-1073 64 8 ( ( PUNCT hjic-1073 64 9 l l NOUN hjic-1073 64 10 - - NOUN hjic-1073 64 11 x7 x7 NOUN hjic-1073 64 12 } } PUNCT hjic-1073 64 13 + + NOUN hjic-1073 64 14 v v NOUN hjic-1073 64 15 - - PUNCT hjic-1073 64 16 xs xs NOUN hjic-1073 64 17 } } PUNCT hjic-1073 64 18 + + PROPN hjic-1073 64 19 ( ( PUNCT hjic-1073 64 20 x7 x7 INTJ hjic-1073 64 21 -x1xs -x1xs VERB hjic-1073 64 22 -x2x6y -x2x6y X hjic-1073 64 23 + + CCONJ hjic-1073 64 24 ( ( PUNCT hjic-1073 64 25 xs xs PROPN hjic-1073 64 26 x3xs x3xs PUNCT hjic-1073 64 27 x4x6 x4x6 PROPN hjic-1073 64 28 } } PUNCT hjic-1073 64 29 ( ( PUNCT hjic-1073 64 30 8) 8) NUM hjic-1073 64 31 and and CCONJ hjic-1073 64 32 minimize minimize VERB hjic-1073 64 33 ft ft NOUN hjic-1073 64 34 or or CCONJ hjic-1073 64 35 f f PROPN hjic-1073 64 36 2 2 NUM hjic-1073 64 37 with with ADP hjic-1073 64 38 respect respect NOUN hjic-1073 64 39 to to ADP hjic-1073 64 40 all all PRON hjic-1073 64 41 of of ADP hjic-1073 64 42 the the DET hjic-1073 64 43 variables variable NOUN hjic-1073 64 44 involved involve VERB hjic-1073 64 45 in in ADP hjic-1073 64 46 each each DET hjic-1073 64 47 case case NOUN hjic-1073 64 48 . . PUNCT hjic-1073 65 1 so so ADV hjic-1073 65 2 , , PUNCT hjic-1073 65 3 for for ADP hjic-1073 65 4 example example NOUN hjic-1073 65 5 , , PUNCT hjic-1073 65 6 using use VERB hjic-1073 65 7 " " PUNCT hjic-1073 65 8 find find VERB hjic-1073 65 9 minimum minimum NOUN hjic-1073 65 10 " " PUNCT hjic-1073 65 11 from from ADP hjic-1073 65 12 " " PUNCT hjic-1073 65 13 mathema mathema ADJ hjic-1073 65 14 tica tica NOUN hjic-1073 65 15 " " PUNCT hjic-1073 65 16 on on ADP hjic-1073 65 17 ft ft ADP hjic-1073 65 18 the the DET hjic-1073 65 19 solution solution NOUN hjic-1073 65 20 ( ( PUNCT hjic-1073 65 21 9 9 NUM hjic-1073 65 22 ) ) PUNCT hjic-1073 65 23 is be AUX hjic-1073 65 24 obtained obtain VERB hjic-1073 65 25 and and CCONJ hjic-1073 65 26 using use VERB hjic-1073 65 27 / / SYM hjic-1073 65 28 2 2 NUM hjic-1073 65 29 gives give VERB hjic-1073 65 30 the the DET hjic-1073 65 31 solution solution NOUN hjic-1073 65 32 notice notice VERB hjic-1073 65 33 that that SCONJ hjic-1073 65 34 the the DET hjic-1073 65 35 solution solution NOUN hjic-1073 65 36 given give VERB hjic-1073 65 37 in in ADP hjic-1073 65 38 eqn.(9 eqn.(9 NUM hjic-1073 65 39 ) ) PUNCT hjic-1073 65 40 is be AUX hjic-1073 65 41 the the DET hjic-1073 65 42 same same ADJ hjic-1073 65 43 as as ADP hjic-1073 65 44 that that PRON hjic-1073 65 45 found find VERB hjic-1073 65 46 by by ADP hjic-1073 65 47 al al PROPN hjic-1073 65 48 . . PUNCT hjic-1073 66 1 the the DET hjic-1073 66 2 similar similar ADJ hjic-1073 66 3 , , PUNCT hjic-1073 66 4 but but CCONJ hjic-1073 66 5 simpler simple ADJ hjic-1073 66 6 example example NOUN hjic-1073 66 7 with with ADP hjic-1073 66 8 l= l= ADJ hjic-1073 66 9 [ [ X hjic-1073 66 10 a.bf a.bf PROPN hjic-1073 66 11 and and CCONJ hjic-1073 66 12 m m PROPN hjic-1073 66 13 = = PUNCT hjic-1073 67 1 [ [ X hjic-1073 67 2 uf uf NOUN hjic-1073 67 3 can can AUX hjic-1073 67 4 be be AUX hjic-1073 67 5 analysed analyse VERB hjic-1073 67 6 algebraicauy algebraicauy NOUN hjic-1073 67 7 to to PART hjic-1073 67 8 quantize quantize VERB hjic-1073 67 9 the the DET hjic-1073 67 10 difference difference NOUN hjic-1073 67 11 between between ADP hjic-1073 67 12 using use VERB hjic-1073 67 13 f f PROPN hjic-1073 67 14 1 1 NUM hjic-1073 67 15 and and CCONJ hjic-1073 67 16 ! ! SYM hjic-1073 67 17 2 2 NUM hjic-1073 67 18 • • NOUN hjic-1073 67 19 thus thus ADV hjic-1073 67 20 , , PUNCT hjic-1073 67 21 for for ADP hjic-1073 67 22 example example NOUN hjic-1073 67 23 , , PUNCT hjic-1073 67 24 taking take VERB hjic-1073 67 25 l l NOUN hjic-1073 67 26 = = PUNCT hjic-1073 68 1 [ [ X hjic-1073 68 2 l,-g.9sf l,-g.9sf PRON hjic-1073 68 3 gives give VERB hjic-1073 68 4 solutions solution NOUN hjic-1073 68 5 x x PUNCT hjic-1073 68 6 = = PUNCT hjic-1073 68 7 2.37165 2.37165 NUM hjic-1073 68 8 and and CCONJ hjic-1073 68 9 x x NOUN hjic-1073 68 10 " " PUNCT hjic-1073 68 11 " " PUNCT hjic-1073 68 12 0.0553169 0.0553169 NUM hjic-1073 68 13 using use VERB hjic-1073 68 14 a a DET hjic-1073 68 15 andf~ andf~ NOUN hjic-1073 68 16 respectively respectively ADV hjic-1073 68 17 . . PUNCT hjic-1073 69 1 ( ( PUNCT hjic-1073 69 2 again again ADV hjic-1073 69 3 using use VERB hjic-1073 69 4 jj jj PROPN hjic-1073 69 5 gives give VERB hjic-1073 69 6 the the DET hjic-1073 69 7 same same ADJ hjic-1073 69 8 solution solution NOUN hjic-1073 69 9 as as ADP hjic-1073 69 10 al al PROPN hjic-1073 69 11 and and CCONJ hjic-1073 69 12 as as ADP hjic-1073 69 13 the the DET hjic-1073 69 14 svd svd PROPN hjic-1073 69 15 formula formula NOUN hjic-1073 69 16 given give VERB hjic-1073 69 17 in in ADP hjic-1073 69 18 example example NOUN hjic-1073 69 19 1 1 NUM hjic-1073 69 20 . . PUNCT hjic-1073 69 21 ) ) PUNCT hjic-1073 70 1 example4 example4 PUNCT hjic-1073 71 1 this this PRON hjic-1073 71 2 is be AUX hjic-1073 71 3 similar similar ADJ hjic-1073 71 4 to to PART hjic-1073 71 5 example example NOUN hjic-1073 71 6 3 3 NUM hjic-1073 71 7 but but CCONJ hjic-1073 71 8 rather rather ADV hjic-1073 71 9 more more ADV hjic-1073 71 10 sophisticated sophisticated ADJ hjic-1073 71 11 ; ; PUNCT hjic-1073 71 12 it it PRON hjic-1073 71 13 is be AUX hjic-1073 71 14 taken take VERB hjic-1073 71 15 from from ADP hjic-1073 71 16 { { PUNCT hjic-1073 71 17 21 21 NUM hjic-1073 71 18 where where SCONJ hjic-1073 71 19 it it PRON hjic-1073 71 20 is be AUX hjic-1073 71 21 analysed analyse VERB hjic-1073 71 22 usingsvd usingsvd NOUN hjic-1073 71 23 , , PUNCT hjic-1073 71 24 r r NOUN hjic-1073 71 25 .. .. PUNCT hjic-1073 71 26 /6 /6 NOUN hjic-1073 71 27 .(6 .(6 PUNCT hjic-1073 72 1 l l NOUN hjic-1073 72 2 l= l= X hjic-1073 73 1 j214 j214 PROPN hjic-1073 73 2 -/'il4 -/'il4 PROPN hjic-1073 73 3 .• .• PROPN hjic-1073 73 4 .fin .fin PROPN hjic-1073 73 5 .fin .fin PUNCT hjic-1073 74 1 m m VERB hjic-1073 75 1 =[ =[ NOUN hjic-1073 75 2 ~ ~ PUNCT hjic-1073 75 3 ] ] X hjic-1073 75 4 · · PUNCT hjic-1073 75 5 · · PUNCT hjic-1073 75 6 - - PUNCT hjic-1073 75 7 .. .. PUNCT hjic-1073 75 8 fi fi NOUN hjic-1073 75 9 using use VERB hjic-1073 75 10 x x X hjic-1073 75 11 0 0 PUNCT hjic-1073 76 1 = = SYM hjic-1073 76 2 0 0 PUNCT hjic-1073 77 1 as as SCONJ hjic-1073 77 2 the the DET hjic-1073 77 3 starting starting NOUN hjic-1073 77 4 approximation approximation NOUN hjic-1073 77 5 in in ADP hjic-1073 77 6 al al PROPN hjic-1073 77 7 gives give VERB hjic-1073 77 8 the the DET hjic-1073 77 9 ls ls ADJ hjic-1073 77 10 solution solution NOUN hjic-1073 77 11 xu xu PROPN hjic-1073 78 1 =[ =[ NOUN hjic-1073 78 2 o.zs2633.o.:zsz633r o.zs2633.o.:zsz633r NOUN hjic-1073 78 3 and and CCONJ hjic-1073 78 4 then then ADV hjic-1073 78 5 proceeding proceed VERB hjic-1073 78 6 to to ADP hjic-1073 78 7 convergence convergence NOUN hjic-1073 78 8 gives give VERB hjic-1073 78 9 the the DET hjic-1073 78 10 tls tls NOUN hjic-1073 78 11 solution solution NOUN hjic-1073 78 12 x x PUNCT hjic-1073 78 13 ns ns NUM hjic-1073 78 14 = = NOUN hjic-1073 78 15 { { PUNCT hjic-1073 78 16 0.408248 0.408248 NUM hjic-1073 78 17 , , PUNCT hjic-1073 78 18 0.408248f 0.408248f NUM hjic-1073 78 19 notice notice VERB hjic-1073 78 20 that that SCONJ hjic-1073 78 21 this this PRON hjic-1073 78 22 is be AUX hjic-1073 78 23 the the DET hjic-1073 78 24 same same ADJ hjic-1073 78 25 as as ADP hjic-1073 78 26 the the DET hjic-1073 78 27 solution solution NOUN hjic-1073 78 28 p! p! PROPN hjic-1073 78 29 .. .. PUNCT hjic-1073 78 30 /6.11 /6.11 PUNCT hjic-1073 79 1 ji;f ji;f ADV hjic-1073 80 1 given give VERB hjic-1073 80 2 in in ADP hjic-1073 80 3 { { PUNCT hjic-1073 80 4 2j 2j NOUN hjic-1073 80 5 . . PUNCT hjic-1073 81 1 jn jn PROPN hjic-1073 81 2 the the DET hjic-1073 81 3 same same ADJ hjic-1073 81 4 manner manner NOUN hjic-1073 81 5 , , PUNCT hjic-1073 81 6 as as ADP hjic-1073 81 7 for for ADP hjic-1073 81 8 the the DET hjic-1073 81 9 previous previous ADJ hjic-1073 81 10 example example NOUN hjic-1073 81 11 , , PUNCT hjic-1073 81 12 setting set VERB hjic-1073 81 13 up up ADP hjic-1073 81 14 the the DET hjic-1073 81 15 appropriate appropriate ADJ hjic-1073 81 16 jj jj NOUN hjic-1073 81 17 and and CCONJ hjic-1073 81 18 using use VERB hjic-1073 81 19 findminimum findminimum NOUN hjic-1073 81 20 gives give VERB hjic-1073 81 21 x x PUNCT hjic-1073 81 22 = = SYM hjic-1073 81 23 ( ( PUNCT hjic-1073 81 24 o.408245 o.408245 PROPN hjic-1073 81 25 , , PUNCT hjic-1073 81 26 0.408425f 0.408425f NOUN hjic-1073 81 27 and and CCONJ hjic-1073 81 28 with with ADP hjic-1073 81 29 the the DET hjic-1073 81 30 appropriate appropriate ADJ hjic-1073 81 31 / / SYM hjic-1073 81 32 2 2 NUM hjic-1073 81 33 the the DET hjic-1073 81 34 solution solution NOUN hjic-1073 81 35 x x PUNCT hjic-1073 81 36 =[ =[ NOUN hjic-1073 81 37 o.34186,0.34186 o.34186,0.34186 PROPN hjic-1073 81 38 t. t. NOUN hjic-1073 81 39 is be AUX hjic-1073 81 40 obtained obtain VERB hjic-1073 81 41 . . PUNCT hjic-1073 82 1 example$ example$ PROPN hjic-1073 82 2 the the DET hjic-1073 82 3 final final ADJ hjic-1073 82 4 example example NOUN hjic-1073 82 5 ts ts ADP hjic-1073 82 6 concerned concerned ADJ hjic-1073 82 7 wltb wltb NOUN hjic-1073 82 8 parameter parameter NOUN hjic-1073 82 9 fitting fitting ADJ hjic-1073 82 10 and and CCONJ hjic-1073 82 11 1s 1s NUM hjic-1073 82 12 raken raken VERB hjic-1073 82 13 from from ADP hjic-1073 82 14 l8j l8j PROPN hjic-1073 82 15 . . PUNCT hjic-1073 83 1 here here ADV hjic-1073 83 2 l l PROPN hjic-1073 84 1 fl fl NUM hjic-1073 84 2 l l NOUN hjic-1073 85 1 i i PRON hjic-1073 85 2 t t VERB hjic-1073 85 3 i i PRON hjic-1073 86 1 = = VERB hjic-1073 87 1 i i PRON hjic-1073 87 2 o o VERB hjic-1073 87 3 o.9 o.9 X hjic-1073 88 1 t.s t.s PROPN hjic-1073 88 2 2.6 2.6 NUM hjic-1073 88 3 3.3 3.3 NUM hjic-1073 88 4 ... ... PUNCT hjic-1073 89 1 l l NOUN hjic-1073 90 1 i i PRON hjic-1073 90 2 i i PRON hjic-1073 91 1 i i VERB hjic-1073 91 2 1 1 NUM hjic-1073 91 3 y y PROPN hjic-1073 91 4 4.4 4.4 NUM hjic-1073 91 5 5 5 NUM hjic-1073 91 6 .. .. SYM hjic-1073 91 7 2 2 NUM hjic-1073 92 1 6.1 6.1 NUM hjic-1073 92 2 65 65 NUM hjic-1073 92 3 7.4 7.4 NUM hjic-1073 92 4 j j PROPN hjic-1073 92 5 m m PROPN hjic-1073 92 6 = = PROPN hjic-1073 92 7 b b ADP hjic-1073 92 8 ~ ~ SYM hjic-1073 92 9 s~4~4~3 s~4~4~3 ADJ hjic-1073 92 10 ~ ~ X hjic-1073 92 11 j~2&2liat5f j~2&2liat5f NOUN hjic-1073 92 12 in in ADP hjic-1073 92 13 dus dus PROPN hjic-1073 92 14 example example NOUN hjic-1073 92 15 the the DET hjic-1073 92 16 first first ADJ hjic-1073 92 17 rolumn rolumn NOUN hjic-1073 92 18 of of ADP hjic-1073 92 19 l l PROPN hjic-1073 92 20 is be AUX hjic-1073 92 21 . . PUNCT hjic-1073 93 1 fixed fix VERB hjic-1073 93 2 and and CCONJ hjic-1073 93 3 so so ADV hjic-1073 93 4 one one NUM hjic-1073 93 5 merhod merhod NOUN hjic-1073 93 6 of of ADP hjic-1073 93 7 proc¢alins proc¢alin NOUN hjic-1073 93 8 is be AUX hjic-1073 93 9 . . PUNCT hjic-1073 94 1 as as SCONJ hjic-1073 94 2 follows follow VERB hjic-1073 94 3 .. .. PUNCT hjic-1073 95 1 f2 f2 PROPN hjic-1073 95 2 } } PUNCT hjic-1073 95 3 ; ; PUNCT hjic-1073 95 4 ilmi ilmi PROPN hjic-1073 95 5 • • PROPN hjic-1073 95 6 > > X hjic-1073 95 7 muhtphed muhtphe VERB hjic-1073 95 8 by by ADP hjic-1073 95 9 a a DET hjic-1073 95 10 su1tabfe su1tabfe NOUN hjic-1073 95 11 ho\ilioelmlder ho\ilioelmlder NOUN hjic-1073 95 12 matnx matnx NOUN hjic-1073 95 13 to to ADP hjic-1073 95 14 & & CCONJ hjic-1073 95 15 •'•e •'•e PROPN hjic-1073 95 16 1he 1he ADJ hjic-1073 95 17 newmatn newmatn PROPN hjic-1073 95 18 : : PUNCT hjic-1073 95 19 t t PROPN hjic-1073 95 20 ( ( PUNCT hjic-1073 95 21 i i NOUN hjic-1073 95 22 ( ( PUNCT hjic-1073 95 23 ) ) PUNCT hjic-1073 95 24 : : PUNCT hjic-1073 95 25 .. .. PUNCT hjic-1073 95 26 16:!28 16:!28 NUM hjic-1073 95 27 t::t.oi•)t t::t.oi•)t NUM hjic-1073 95 28 ) ) PUNCT hjic-1073 95 29 ii ii PROPN hjic-1073 95 30 ' ' NUM hjic-1073 95 31 1004 1004 NUM hjic-1073 95 32 0 0 NUM hjic-1073 95 33 · · SYM hjic-1073 95 34 4.68666 4.68666 NUM hjic-1073 95 35 : : PUNCT hjic-1073 95 36 : : PUNCT hjic-1073 95 37 ! ! PUNCT hjic-1073 95 38 .7174;'\ .7174;'\ PUNCT hjic-1073 95 39 0 0 PUNCT hjic-1073 96 1 -~.78666 -~.78666 INTJ hjic-1073 96 2 l7174s l7174s ADP hjic-1073 96 3 0 0 NUM hjic-1073 96 4 · · PUNCT hjic-1073 96 5 : : PUNCT hjic-1073 96 6 : : PUNCT hjic-1073 96 7 ! ! PUNCT hjic-1073 96 8 .. .. PUNCT hjic-1073 97 1 9smt\ 9smt\ X hjic-1073 97 2 1.917451 1.917451 NUM hjic-1073 97 3 0 0 NUM hjic-1073 98 1 .;!,;86n .;!,;86n NOUN hjic-1073 98 2 , , PUNCT hjic-1073 98 3 0.8j14j6 0.8j14j6 NOUN hjic-1073 98 4 0 0 NUM hjic-1073 99 1 -u866b -u866b PROPN hjic-1073 99 2 j.ol745 j.ol745 PROPN hjic-1073 99 3 0 0 NUM hjic-1073 100 1 -0.~86656 -0.~86656 NOUN hjic-1073 100 2 0 0 NUM hjic-1073 101 1 lf74j6 lf74j6 ADJ hjic-1073 101 2 0 0 NUM hjic-1073 102 1 0.513344 0.513344 NUM hjic-1073 102 2 0.117446 0.117446 NUM hjic-1073 102 3 0 0 NUM hjic-1073 102 4 0.913~44 0.913~44 NUM hjic-1073 102 5 .0.2825$4 .0.2825$4 PUNCT hjic-1073 102 6 0 0 X hjic-1073 102 7 1.81334 1.81334 NUM hjic-1073 102 8 · · SYM hjic-1073 102 9 1.18:!5~ 1.18:!5~ NOUN hjic-1073 102 10 and and CCONJ hjic-1073 102 11 algorithm algorithm NOUN hjic-1073 102 12 a a DET hjic-1073 102 13 1 1 NUM hjic-1073 102 14 is be AUX hjic-1073 102 15 now now ADV hjic-1073 102 16 apphcd apphcd ADJ hjic-1073 102 17 to to ADP hjic-1073 102 18 the the DET hjic-1073 102 19 ~ubmatm ~ubmatm NUM hjic-1073 102 20 . . PROPN hjic-1073 102 21 obtained obtain VERB hjic-1073 102 22 by by ADP hjic-1073 102 23 deleting delete VERB hjic-1073 102 24 the the DET hjic-1073 102 25 first first ADJ hjic-1073 102 26 row row NOUN hjic-1073 102 27 and and CCONJ hjic-1073 102 28 column column NOUN hjic-1073 102 29 of of ADP hjic-1073 102 30 the the DET hjic-1073 102 31 above above ADJ hjic-1073 102 32 matrix matrix NOUN hjic-1073 102 33 . . PUNCT hjic-1073 103 1 to to PART hjic-1073 103 2 give give VERB hjic-1073 103 3 the the DET hjic-1073 103 4 : : PUNCT hjic-1073 103 5 .«ond .«ond PROPN hjic-1073 103 6 componenr componenr PROPN hjic-1073 103 7 .t .t PROPN hjic-1073 103 8 : : PUNCT hjic-1073 103 9 of of ADP hjic-1073 103 10 the the DET hjic-1073 103 11 solution solution NOUN hjic-1073 103 12 vector vector NOUN hjic-1073 103 13 x. x. NOUN hjic-1073 103 14 the the DET hjic-1073 103 15 first first ADJ hjic-1073 103 16 component component NOUN hjic-1073 103 17 .t1 .t1 NOUN hjic-1073 103 18 of of ADP hjic-1073 103 19 x x X hjic-1073 103 20 ' ' PUNCT hjic-1073 103 21 " " PUNCT hjic-1073 103 22 then then ADV hjic-1073 103 23 obtained obtain VERB hjic-1073 103 24 from from ADP hjic-1073 103 25 .3.16228 .3.16228 PROPN hjic-1073 103 26 xi xi PROPN hjic-1073 103 27 : : PUNCT hjic-1073 103 28 : : PUNCT hjic-1073 103 29 : : PUNCT hjic-1073 103 30 j j PROPN hjic-1073 103 31 1.7004 1.7004 NUM hjic-1073 103 32 -12 -12 PROPN hjic-1073 103 33 .. .. PUNCT hjic-1073 103 34 07q9 07q9 NUM hjic-1073 103 35 t t PROPN hjic-1073 103 36 : : PUNCT hjic-1073 103 37 · · PUNCT hjic-1073 103 38 ; ; PUNCT hjic-1073 103 39 in in ADP hjic-1073 103 40 this this DET hjic-1073 103 41 way way NOUN hjic-1073 103 42 x x X hjic-1073 103 43 : : PUNCT hjic-1073 103 44 : : PUNCT hjic-1073 103 45 : : PUNCT hjic-1073 103 46 .{5.7840~.-0.sj55o2f .{5.7840~.-0.sj55o2f PROPN hjic-1073 103 47 is be AUX hjic-1073 103 48 obtained obtain VERB hjic-1073 103 49 . . PUNCT hjic-1073 104 1 direct direct ADJ hjic-1073 104 2 minimizattt~~l minimizattt~~l PROPN hjic-1073 105 1 ~an ~an X hjic-1073 105 2 oth.o oth.o PROPN hjic-1073 105 3 be be AUX hjic-1073 105 4 u.rma.l1rnm f·>rma.l1rnm PROPN hjic-1073 114 17 m&ut'e~ m&ut'e~ PROPN hjic-1073 114 18 4 4 NUM hjic-1073 114 19 .andb .andb NOUN hjic-1073 114 20 a.b.c.r.s.cc./lu a.b.c.r.s.cc./lu PROPN hjic-1073 114 21 .t .t PROPN hjic-1073 114 22 . . PUNCT hjic-1073 115 1 matn matn PROPN hjic-1073 115 2 .. .. PUNCT hjic-1073 115 3 c:1o c:1o NOUN hjic-1073 115 4 dchnc.ltn dchnc.ltn X hjic-1073 115 5 · · SYM hjic-1073 115 6 \~nj \~nj X hjic-1073 115 7 , , PUNCT hjic-1073 115 8 , , PUNCT hjic-1073 115 9 ... ... PUNCT hjic-1073 115 10 ' ' PUNCT hjic-1073 115 11 a• a• PROPN hjic-1073 115 12 ai ai VERB hjic-1073 115 13 . . PUNCT hjic-1073 115 14 a. a. NOUN hjic-1073 115 15 ? ? PUNCT hjic-1073 116 1 s\'0 s\'0 NOUN hjic-1073 116 2 trai\.'j)i'tk trai\.'j)i'tk NOUN hjic-1073 116 3 of of ADP hjic-1073 116 4 matn• matn• ADJ hjic-1073 116 5 a a DET hjic-1073 116 6 ~udn ~udn NOUN hjic-1073 116 7 - - PUNCT hjic-1073 116 8 mvc mvc NOUN hjic-1073 116 9 : : PUNCT hjic-1073 116 10 tk tk PROPN hjic-1073 116 11 , , PUNCT hjic-1073 116 12 , , PUNCT hjic-1073 116 13 f f PROPN hjic-1073 116 14 m.auu m.auu PROPN hjic-1073 116 15 .. .. PUNCT hjic-1073 116 16 -\ -\ PROPN hjic-1073 116 17 algunthrll\ algunthrll\ PROPN hjic-1073 116 18 frnrn frnrn PROPN hjic-1073 116 19 j j PROPN hjic-1073 116 20 ( ( PUNCT hjic-1073 116 21 ) ) PUNCT hjic-1073 116 22 ) ) PUNCT hjic-1073 116 23 \lflgul.u \lflgul.u VERB hjic-1073 116 24 v.-luc v.-luc PROPN hjic-1073 116 25 d<-<:•'fllp'"'tll<>n d<-<:•'fllp'"'tll<>n NOUN hjic-1073 116 26 ' ' PART hjic-1073 116 27 .:nttpr•nc .:nttpr•nc NUM hjic-1073 116 28 : : PUNCT hjic-1073 117 1 nl~ nl~ PROPN hjic-1073 117 2 ut ut PROPN hjic-1073 117 3 \('d<'f \('d<'f PROPN hjic-1073 117 4 ' ' PUNCT hjic-1073 117 5 " " PUNCT hjic-1073 117 6 ' ' PUNCT hjic-1073 117 7 m.jlfl\ m.jlfl\ X hjic-1073 117 8 \ \ PUNCT hjic-1073 118 1 k.al k.al PROPN hjic-1073 118 2 - - PUNCT hjic-1073 118 3 f f PROPN hjic-1073 118 4 ~u.uc:~ ~u.uc:~ NUM hjic-1073 118 5 lul lul NOUN hjic-1073 118 6 , , PUNCT hjic-1073 118 7 tllc.- tllc.- PROPN hjic-1073 118 8 . . PROPN hjic-1073 118 9 .. .. PUNCT hjic-1073 119 1 t t PROPN hjic-1073 119 2 -.qu.ltc -.qu.ltc PUNCT hjic-1073 119 3 : : PUNCT hjic-1073 119 4 t.o t.o PROPN hjic-1073 119 5 nmmny nmmny PROPN hjic-1073 119 6 mje1 mje1 PROPN hjic-1073 119 7 . . PUNCT hjic-1073 120 1 70 70 NUM hjic-1073 120 2 e e NOUN hjic-1073 120 3 sums sum NOUN hjic-1073 120 4 of of ADP hjic-1073 120 5 squares square NOUN hjic-1073 120 6 defined define VERB hjic-1073 120 7 in in ADP hjic-1073 120 8 eqns eqns PROPN hjic-1073 120 9 . . PUNCT hjic-1073 121 1 ( ( PUNCT hjic-1073 121 2 7 7 NUM hjic-1073 121 3 ) ) PUNCT hjic-1073 121 4 and and CCONJ hjic-1073 121 5 ( ( PUNCT hjic-1073 121 6 8) 8) NUM hjic-1073 121 7 euclidian euclidian ADJ hjic-1073 121 8 norm norm NOUN hjic-1073 121 9 of of ADP hjic-1073 121 10 a a DET hjic-1073 121 11 euclidian euclidian ADJ hjic-1073 121 12 norm norm NOUN hjic-1073 121 13 of of ADP hjic-1073 121 14 residual residual ADJ hjic-1073 121 15 error error NOUN hjic-1073 121 16 in in ADP hjic-1073 121 17 solution solution NOUN hjic-1073 121 18 of of ADP hjic-1073 121 19 amre amre PROPN hjic-1073 121 20 m m PROPN hjic-1073 121 21 , , PUNCT hjic-1073 121 22 n n CCONJ hjic-1073 121 23 , , PUNCT hjic-1073 121 24 p p NOUN hjic-1073 121 25 integers integer NOUN hjic-1073 121 26 used use VERB hjic-1073 121 27 to to PART hjic-1073 121 28 give give VERB hjic-1073 121 29 order order NOUN hjic-1073 121 30 of of ADP hjic-1073 121 31 matrices matrix NOUN hjic-1073 121 32 references reference NOUN hjic-1073 121 33 1 1 NUM hjic-1073 121 34 . . PUNCT hjic-1073 122 1 lawson lawson PROPN hjic-1073 122 2 l. l. PROPN hjic-1073 122 3 and and CCONJ hjic-1073 122 4 hanson hanson PROPN hjic-1073 122 5 j. j. PROPN hjic-1073 122 6 : : PUNCT hjic-1073 122 7 solving solve VERB hjic-1073 122 8 least least ADJ hjic-1073 122 9 squares square NOUN hjic-1073 122 10 problems problem NOUN hjic-1073 122 11 , , PUNCT hjic-1073 122 12 prentice prentice NOUN hjic-1073 122 13 - - PUNCT hjic-1073 122 14 hall hall NOUN hjic-1073 122 15 , , PUNCT hjic-1073 122 16 inc inc PROPN hjic-1073 122 17 . . PROPN hjic-1073 122 18 , , PUNCT hjic-1073 122 19 englewood englewood PROPN hjic-1073 122 20 cliffs cliffs PROPN hjic-1073 122 21 , , PUNCT hjic-1073 122 22 new new PROPN hjic-1073 122 23 jersey jersey PROPN hjic-1073 122 24 , , PUNCT hjic-1073 122 25 1974 1974 NUM hjic-1073 122 26 . . PUNCT hjic-1073 123 1 2 2 X hjic-1073 123 2 . . X hjic-1073 123 3 van van PROPN hjic-1073 123 4 huffel huffel PROPN hjic-1073 123 5 s. s. PROPN hjic-1073 123 6 and and CCONJ hjic-1073 123 7 vande vande PROPN hjic-1073 123 8 walle walle PROPN hjic-1073 123 9 j. j. PROPN hjic-1073 123 10 : : PUNCT hjic-1073 123 11 the the DET hjic-1073 123 12 total total ADJ hjic-1073 123 13 least least ADJ hjic-1073 123 14 squares square NOUN hjic-1073 123 15 problem problem NOUN hjic-1073 123 16 : : PUNCT hjic-1073 123 17 computational computational ADJ hjic-1073 123 18 aspects aspect NOUN hjic-1073 123 19 and and CCONJ hjic-1073 123 20 analysis analysis NOUN hjic-1073 123 21 , , PUNCT hjic-1073 123 22 siam siam PROPN hjic-1073 123 23 philadelphia philadelphia PROPN hjic-1073 123 24 , , PUNCT hjic-1073 123 25 1991 1991 NUM hjic-1073 123 26 . . PUNCT hjic-1073 124 1 3 3 X hjic-1073 124 2 . . X hjic-1073 124 3 de de PROPN hjic-1073 124 4 moor moor PROPN hjic-1073 124 5 b. b. PROPN hjic-1073 124 6 and and CCONJ hjic-1073 124 7 david david PROPN hjic-1073 124 8 j. j. PROPN hjic-1073 124 9 : : PUNCT hjic-1073 124 10 systems system NOUN hjic-1073 124 11 and and CCONJ hjic-1073 124 12 control control NOUN hjic-1073 124 13 letters letter NOUN hjic-1073 124 14 , , PUNCT hjic-1073 124 15 l992 l992 PROPN hjic-1073 124 16 , , PUNCT hjic-1073 124 17 18 18 NUM hjic-1073 124 18 , , PUNCT hjic-1073 124 19 329 329 NUM hjic-1073 124 20 - - SYM hjic-1073 124 21 337 337 NUM hjic-1073 124 22 . . PUNCT hjic-1073 125 1 4 4 NUM hjic-1073 125 2 . . X hjic-1073 125 3 lancaster lancaster PROPN hjic-1073 125 4 p. p. PROPN hjic-1073 125 5 and and CCONJ hjic-1073 125 6 rodman rodman PROPN hjic-1073 125 7 l. l. PROPN hjic-1073 125 8 : : PUNCT hjic-1073 125 9 algebraic algebraic PROPN hjic-1073 125 10 riccati riccati PROPN hjic-1073 125 11 equations equation NOUN hjic-1073 125 12 , , PUNCT hjic-1073 125 13 clarendon clarendon PROPN hjic-1073 125 14 press press PROPN hjic-1073 125 15 oxford oxford PROPN hjic-1073 125 16 , , PUNCT hjic-1073 125 17 1995 1995 NUM hjic-1073 125 18 . . PUNCT hjic-1073 126 1 .5 .5 NUM hjic-1073 126 2 . . PUNCT hjic-1073 127 1 barnett barnett PROPN hjic-1073 127 2 s. s. PROPN hjic-1073 127 3 and and CCONJ hjic-1073 127 4 storey storey PROPN hjic-1073 127 5 c. c. PROPN hjic-1073 127 6 : : PUNCT hjic-1073 127 7 matrix matrix NOUN hjic-1073 127 8 methods method NOUN hjic-1073 127 9 in in ADP hjic-1073 127 10 stability stability NOUN hjic-1073 127 11 theory theory NOUN hjic-1073 127 12 , , PUNCT hjic-1073 127 13 thomas thomas PROPN hjic-1073 127 14 nelson nelson PROPN hjic-1073 127 15 and and CCONJ hjic-1073 127 16 sons son NOUN hjic-1073 127 17 limited limit VERB hjic-1073 127 18 , , PUNCT hjic-1073 127 19 1970 1970 NUM hjic-1073 127 20 . . PUNCT hjic-1073 128 1 6 6 NUM hjic-1073 128 2 . . X hjic-1073 128 3 storey storey PROPN hjic-1073 128 4 c. c. PROPN hjic-1073 128 5 : : PUNCT hjic-1073 128 6 modified modified PROPN hjic-1073 128 7 newton newton PROPN hjic-1073 128 8 methods method NOUN hjic-1073 128 9 for for ADP hjic-1073 128 10 the the DET hjic-1073 128 11 algebraic algebraic ADJ hjic-1073 128 12 matrix matrix NOUN hjic-1073 128 13 riccati riccati NOUN hjic-1073 128 14 equation equation NOUN hjic-1073 128 15 , , PUNCT hjic-1073 128 16 part part NOUN hjic-1073 128 17 1 1 NUM hjic-1073 128 18 : : PUNCT hjic-1073 128 19 hung.j hung.j PROPN hjic-1073 128 20 . . PUNCT hjic-1073 129 1 ind ind PROPN hjic-1073 129 2 . . PUNCT hjic-1073 130 1 chern chern PROPN hjic-1073 130 2 . . PROPN hjic-1073 130 3 , , PUNCT hjic-1073 130 4 i997 i997 PROPN hjic-1073 130 5 , , PUNCT hjic-1073 130 6 25,305 25,305 NUM hjic-1073 130 7 - - SYM hjic-1073 130 8 308 308 NUM hjic-1073 130 9 , , PUNCT hjic-1073 130 10 part2 part2 PROPN hjic-1073 130 11 : : PUNCT hjic-1073 130 12 ibid ibid NOUN hjic-1073 130 13 . . PUNCT hjic-1073 130 14 , , PUNCT hjic-1073 130 15 i998 i998 PROPN hjic-1073 130 16 , , PUNCT hjic-1073 130 17 26,309 26,309 NUM hjic-1073 130 18 - - SYM hjic-1073 130 19 314 314 NUM hjic-1073 130 20 , , PUNCT hjic-1073 130 21 part part NOUN hjic-1073 130 22 3 3 NUM hjic-1073 130 23 : : PUNCT hjic-1073 130 24 ibid ibid NOUN hjic-1073 130 25 . . PUNCT hjic-1073 131 1 ,j999 ,j999 PROPN hjic-1073 131 2 , , PUNCT hjic-1073 131 3 27 27 NUM hjic-1073 131 4 , , PUNCT hjic-1073 131 5 301 301 NUM hjic-1073 131 6 - - SYM hjic-1073 131 7 305 305 NUM hjic-1073 131 8 , , PUNCT hjic-1073 131 9 part part NOUN hjic-1073 131 10 4 4 NUM hjic-1073 131 11 : : PUNCT hjic-1073 131 12 ibid ibid NOUN hjic-1073 131 13 . . PUNCT hjic-1073 131 14 , , PUNCT hjic-1073 131 15 2000 2000 NUM hjic-1073 131 16 , , PUNCT hjic-1073 131 17 28 28 NUM hjic-1073 131 18 , , PUNCT hjic-1073 131 19 277 277 NUM hjic-1073 131 20 - - SYM hjic-1073 131 21 280 280 NUM hjic-1073 131 22 . . NOUN hjic-1073 132 1 7 7 NUM hjic-1073 132 2 . . NUM hjic-1073 132 3 wolds wold NOUN hjic-1073 132 4 . . PUNCT hjic-1073 132 5 , , PUNCT hjic-1073 132 6 ruhe ruhe PROPN hjic-1073 132 7 a. a. PROPN hjic-1073 132 8 , , PUNCT hjic-1073 132 9 wold wold PROPN hjic-1073 132 10 s. s. PROPN hjic-1073 132 11 and and CCONJ hjic-1073 132 12 dunn dunn PROPN hjic-1073 132 13 iii iii PROPN hjic-1073 132 14 w.j w.j PROPN hjic-1073 132 15 . . PROPN hjic-1073 132 16 : : PUNCT hjic-1073 133 1 siamj siamj NOUN hjic-1073 133 2 . . PUNCT hjic-1073 134 1 sci sci PROPN hjic-1073 134 2 . . PROPN hjic-1073 134 3 stat stat PROPN hjic-1073 134 4 . . PUNCT hjic-1073 135 1 comput comput NOUN hjic-1073 135 2 . . PUNCT hjic-1073 135 3 , , PUNCT hjic-1073 136 1 1984,5,735 1984,5,735 PROPN hjic-1073 136 2 - - PUNCT hjic-1073 136 3 743 743 NUM hjic-1073 136 4 . . NOUN hjic-1073 136 5 8 8 NUM hjic-1073 136 6 . . PUNCT hjic-1073 136 7 luus luus PROPN hjic-1073 136 8 r. r. PROPN hjic-1073 136 9 and and CCONJ hjic-1073 136 10 hernaez hernaez PROPN hjic-1073 136 11 h. h. PROPN hjic-1073 136 12 : : PUNCT hjic-1073 137 1 hung.j hung.j PROPN hjic-1073 137 2 . . PUNCT hjic-1073 138 1 ind ind PROPN hjic-1073 138 2 . . PUNCT hjic-1073 139 1 chern chern PROPN hjic-1073 139 2 . . PROPN hjic-1073 139 3 , , PUNCT hjic-1073 139 4 2000,28,201 2000,28,201 NOUN hjic-1073 139 5 - - SYM hjic-1073 139 6 207 207 NUM hjic-1073 139 7 . . PUNCT hjic-1073 140 1 appendix appendix ADJ hjic-1073 140 2 algorithm algorithm NOUN hjic-1073 140 3 ai ai VERB hjic-1073 140 4 to to PART hjic-1073 140 5 solve solve VERB hjic-1073 140 6 the the DET hjic-1073 140 7 general general ADJ hjic-1073 140 8 amre amre PROPN hjic-1073 140 9 xpx xpx PROPN hjic-1073 141 1 + + CCONJ hjic-1073 141 2 qx qx PROPN hjic-1073 141 3 + + NUM hjic-1073 141 4 xf xf PROPN hjic-1073 142 1 + + CCONJ hjic-1073 142 2 g g PROPN hjic-1073 142 3 = = SYM hjic-1073 142 4 0 0 PUNCT hjic-1073 142 5 let let VERB hjic-1073 142 6 x x SYM hjic-1073 142 7 0 0 PUNCT hjic-1073 142 8 be be AUX hjic-1073 142 9 an an DET hjic-1073 142 10 approximate approximate ADJ hjic-1073 142 11 solution solution NOUN hjic-1073 142 12 . . PUNCT hjic-1073 143 1 let let VERB hjic-1073 143 2 i i PRON hjic-1073 143 3 = = NOUN hjic-1073 143 4 0 0 NUM hjic-1073 143 5 compute compute NOUN hjic-1073 143 6 : : PUNCT hjic-1073 143 7 a1 a1 PROPN hjic-1073 143 8 = = PROPN hjic-1073 143 9 x1p+q x1p+q PROPN hjic-1073 143 10 b1 b1 NOUN hjic-1073 143 11 = = PRON hjic-1073 143 12 px1 px1 VERB hjic-1073 143 13 + + NOUN hjic-1073 143 14 f f X hjic-1073 143 15 c c NOUN hjic-1073 143 16 , , PUNCT hjic-1073 143 17 = = NOUN hjic-1073 143 18 x1px1 x1px1 X hjic-1073 143 19 -g -g PUNCT hjic-1073 143 20 r r NOUN hjic-1073 143 21 ; ; PUNCT hjic-1073 143 22 =( =( ADJ hjic-1073 143 23 in in ADP hjic-1073 143 24 -a;)-1 -a;)-1 PRON hjic-1073 143 25 s s PART hjic-1073 143 26 ; ; PUNCT hjic-1073 143 27 =( =( NOUN hjic-1073 143 28 inb;)-1 inb;)-1 NOUN hjic-1073 143 29 a1 a1 NOUN hjic-1073 143 30 = = X hjic-1073 143 31 2r1 2r1 NUM hjic-1073 143 32 -in -in X hjic-1073 143 33 { { PUNCT hjic-1073 143 34 31 31 NUM hjic-1073 143 35 = = SYM hjic-1073 143 36 2s1 2s1 NUM hjic-1073 143 37 -in -in NOUN hjic-1073 143 38 m m PROPN hjic-1073 143 39 1 1 NUM hjic-1073 143 40 = = PROPN hjic-1073 143 41 -2r1c1s1 -2r1c1s1 PROPN hjic-1073 143 42 t t PROPN hjic-1073 143 43 1 1 NUM hjic-1073 143 44 < < X hjic-1073 143 45 1l 1l NUM hjic-1073 143 46 = = NOUN hjic-1073 143 47 m m VERB hjic-1073 143 48 1 1 NUM hjic-1073 143 49 tz tz NOUN hjic-1073 143 50 ( ( PUNCT hjic-1073 143 51 i i NOUN hjic-1073 143 52 ) ) PUNCT hjic-1073 143 53 = = PUNCT hjic-1073 144 1 ~ ~ PUNCT hjic-1073 144 2 (; (; X hjic-1073 144 3 } } PUNCT hjic-1073 144 4 + + CCONJ hjic-1073 144 5 a;~