id sid tid token lemma pos cana-1056 1 1 communications communication NOUN cana-1056 1 2 on on ADP cana-1056 1 3 applied apply VERB cana-1056 1 4 nonlinear nonlinear ADJ cana-1056 1 5 analysis analysis NOUN cana-1056 1 6 issn issn NOUN cana-1056 1 7 : : PUNCT cana-1056 1 8 1074 1074 NUM cana-1056 1 9 - - PUNCT cana-1056 1 10 133x 133x NUM cana-1056 1 11 vol vol NOUN cana-1056 1 12 31 31 NUM cana-1056 1 13 no no NOUN cana-1056 1 14 . . PUNCT cana-1056 2 1 5s 5s NUM cana-1056 2 2 ( ( PUNCT cana-1056 2 3 2024 2024 NUM cana-1056 2 4 ) ) PUNCT cana-1056 2 5 372 372 NUM cana-1056 2 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 2 7 a a DET cana-1056 2 8 new new ADJ cana-1056 2 9 modified modify VERB cana-1056 2 10 secant secant ADJ cana-1056 2 11 condition condition NOUN cana-1056 2 12 for for ADP cana-1056 2 13 non non ADJ cana-1056 2 14 - - ADJ cana-1056 2 15 linear linear ADJ cana-1056 2 16 conjugate conjugate ADJ cana-1056 2 17 gradient gradient NOUN cana-1056 2 18 methods method NOUN cana-1056 2 19 with with ADP cana-1056 2 20 global global ADJ cana-1056 2 21 convergence convergence NOUN cana-1056 2 22 farhan farhan PROPN cana-1056 2 23 khalaf khalaf PROPN cana-1056 2 24 muord1 muord1 PROPN cana-1056 2 25 , , PUNCT cana-1056 2 26 muna muna PROPN cana-1056 2 27 m. m. PROPN cana-1056 2 28 m. m. PROPN cana-1056 2 29 ali2 ali2 PROPN cana-1056 2 30 1,2 1,2 NUM cana-1056 2 31 department department NOUN cana-1056 2 32 of of ADP cana-1056 2 33 mathematics mathematic NOUN cana-1056 2 34 , , PUNCT cana-1056 2 35 college college NOUN cana-1056 2 36 of of ADP cana-1056 2 37 computer computer NOUN cana-1056 2 38 science science NOUN cana-1056 2 39 and and CCONJ cana-1056 2 40 mathematics mathematics PROPN cana-1056 2 41 , , PUNCT cana-1056 2 42 mosul mosul PROPN cana-1056 2 43 university university PROPN cana-1056 2 44 , , PUNCT cana-1056 2 45 mosul mosul PROPN cana-1056 2 46 , , PUNCT cana-1056 2 47 iraq iraq PROPN cana-1056 2 48 . . PUNCT cana-1056 3 1 1munamoh74@uomosul.edu.iq 1munamoh74@uomosul.edu.iq NUM cana-1056 3 2 article article NOUN cana-1056 3 3 history history NOUN cana-1056 3 4 : : PUNCT cana-1056 3 5 received receive VERB cana-1056 3 6 : : PUNCT cana-1056 3 7 16 16 NUM cana-1056 3 8 - - SYM cana-1056 3 9 05 05 NUM cana-1056 3 10 - - PUNCT cana-1056 3 11 2024 2024 NUM cana-1056 3 12 revised revise VERB cana-1056 3 13 : : PUNCT cana-1056 3 14 23 23 NUM cana-1056 3 15 - - SYM cana-1056 3 16 06 06 NUM cana-1056 3 17 - - PUNCT cana-1056 3 18 2024 2024 NUM cana-1056 3 19 accepted accept VERB cana-1056 3 20 : : PUNCT cana-1056 3 21 11 11 NUM cana-1056 3 22 - - SYM cana-1056 3 23 07 07 NUM cana-1056 3 24 - - PUNCT cana-1056 3 25 2024 2024 NUM cana-1056 3 26 abstract abstract NOUN cana-1056 3 27 : : PUNCT cana-1056 3 28 the the DET cana-1056 3 29 conjugate conjugate ADJ cana-1056 3 30 gradient gradient NOUN cana-1056 3 31 methods(cgm methods(cgm PROPN cana-1056 3 32 ) ) PUNCT cana-1056 3 33 are be AUX cana-1056 3 34 well well ADV cana-1056 3 35 - - PUNCT cana-1056 3 36 recognized recognize VERB cana-1056 3 37 techniques technique NOUN cana-1056 3 38 for for ADP cana-1056 3 39 handling handle VERB cana-1056 3 40 nonlinear nonlinear ADJ cana-1056 3 41 optimization optimization NOUN cana-1056 3 42 problems problem NOUN cana-1056 3 43 . . PUNCT cana-1056 4 1 dai dai PROPN cana-1056 4 2 and and CCONJ cana-1056 4 3 liao liao PROPN cana-1056 4 4 ( ( PUNCT cana-1056 4 5 2001 2001 NUM cana-1056 4 6 ) ) PUNCT cana-1056 4 7 employ employ VERB cana-1056 4 8 the the DET cana-1056 4 9 secant secant ADJ cana-1056 4 10 condition condition NOUN cana-1056 4 11 approach approach NOUN cana-1056 4 12 , , PUNCT cana-1056 4 13 this this DET cana-1056 4 14 study study NOUN cana-1056 4 15 utilizes utilize VERB cana-1056 4 16 the the DET cana-1056 4 17 modified modified ADJ cana-1056 4 18 secant secant ADJ cana-1056 4 19 condition condition NOUN cana-1056 4 20 proposed propose VERB cana-1056 4 21 by by ADP cana-1056 4 22 yabe yabe PROPN cana-1056 4 23 - - PUNCT cana-1056 4 24 takano takano PROPN cana-1056 4 25 ( ( PUNCT cana-1056 4 26 2004 2004 NUM cana-1056 4 27 ) ) PUNCT cana-1056 4 28 and and CCONJ cana-1056 4 29 zhang zhang PROPN cana-1056 4 30 and and CCONJ cana-1056 4 31 xu xu PROPN cana-1056 4 32 ( ( PUNCT cana-1056 4 33 2001 2001 NUM cana-1056 4 34 ) ) PUNCT cana-1056 4 35 , , PUNCT cana-1056 4 36 which which PRON cana-1056 4 37 is be AUX cana-1056 4 38 satisfied satisfied ADJ cana-1056 4 39 at at ADP cana-1056 4 40 each each DET cana-1056 4 41 iteration iteration NOUN cana-1056 4 42 through through ADP cana-1056 4 43 the the DET cana-1056 4 44 implementation implementation NOUN cana-1056 4 45 of of ADP cana-1056 4 46 the the DET cana-1056 4 47 strong strong ADJ cana-1056 4 48 wolf wolf NOUN cana-1056 4 49 - - PUNCT cana-1056 4 50 line line NOUN cana-1056 4 51 search search NOUN cana-1056 4 52 condition condition NOUN cana-1056 4 53 . . PUNCT cana-1056 5 1 additionally additionally ADV cana-1056 5 2 , , PUNCT cana-1056 5 3 please please INTJ cana-1056 5 4 provide provide VERB cana-1056 5 5 three three NUM cana-1056 5 6 novel novel ADJ cana-1056 5 7 categories category NOUN cana-1056 5 8 of of ADP cana-1056 5 9 conjugate conjugate ADJ cana-1056 5 10 gradient gradient ADJ cana-1056 5 11 algorithms algorithm NOUN cana-1056 5 12 of of ADP cana-1056 5 13 this this DET cana-1056 5 14 nature nature NOUN cana-1056 5 15 . . PUNCT cana-1056 6 1 we we PRON cana-1056 6 2 examined examine VERB cana-1056 6 3 15 15 NUM cana-1056 6 4 well well ADV cana-1056 6 5 - - PUNCT cana-1056 6 6 known know VERB cana-1056 6 7 test test NOUN cana-1056 6 8 functions function NOUN cana-1056 6 9 . . PUNCT cana-1056 7 1 this this DET cana-1056 7 2 novel novel ADJ cana-1056 7 3 approach approach NOUN cana-1056 7 4 utilises utilise VERB cana-1056 7 5 the the DET cana-1056 7 6 existing exist VERB cana-1056 7 7 gradient gradient NOUN cana-1056 7 8 and and CCONJ cana-1056 7 9 function function NOUN cana-1056 7 10 value value NOUN cana-1056 7 11 to to PART cana-1056 7 12 accurately accurately ADV cana-1056 7 13 approximate approximate VERB cana-1056 7 14 the the DET cana-1056 7 15 goal goal NOUN cana-1056 7 16 function function NOUN cana-1056 7 17 with with ADP cana-1056 7 18 high high ADJ cana-1056 7 19 - - PUNCT cana-1056 7 20 order order NOUN cana-1056 7 21 precision precision NOUN cana-1056 7 22 . . PUNCT cana-1056 8 1 the the DET cana-1056 8 2 worldwide worldwide ADJ cana-1056 8 3 convergence convergence NOUN cana-1056 8 4 of of ADP cana-1056 8 5 our our PRON cana-1056 8 6 novel novel ADJ cana-1056 8 7 algorithms algorithm NOUN cana-1056 8 8 is be AUX cana-1056 8 9 demonstrated demonstrate VERB cana-1056 8 10 under under ADP cana-1056 8 11 certain certain ADJ cana-1056 8 12 conditions condition NOUN cana-1056 8 13 . . PUNCT cana-1056 9 1 numerical numerical ADJ cana-1056 9 2 results result NOUN cana-1056 9 3 are be AUX cana-1056 9 4 provided provide VERB cana-1056 9 5 , , PUNCT cana-1056 9 6 and and CCONJ cana-1056 9 7 the the DET cana-1056 9 8 efficiency efficiency NOUN cana-1056 9 9 is be AUX cana-1056 9 10 proven prove VERB cana-1056 9 11 by by ADP cana-1056 9 12 comparing compare VERB cana-1056 9 13 it it PRON cana-1056 9 14 to to ADP cana-1056 9 15 other other ADJ cana-1056 9 16 approaches approach NOUN cana-1056 9 17 . . PUNCT cana-1056 10 1 keywords keyword NOUN cana-1056 10 2 : : PUNCT cana-1056 10 3 conjugate conjugate ADJ cana-1056 10 4 gradient gradient NOUN cana-1056 10 5 technique technique NOUN cana-1056 10 6 , , PUNCT cana-1056 10 7 un un ADJ cana-1056 10 8 - - ADJ cana-1056 10 9 constrained constrain VERB cana-1056 10 10 optimization optimization NOUN cana-1056 10 11 , , PUNCT cana-1056 10 12 numerical numerical ADJ cana-1056 10 13 studies study NOUN cana-1056 10 14 , , PUNCT cana-1056 10 15 preconditioning precondition VERB cana-1056 10 16 , , PUNCT cana-1056 10 17 sufficient sufficient ADJ cana-1056 10 18 descent descent NOUN cana-1056 10 19 condition condition NOUN cana-1056 10 20 , , PUNCT cana-1056 10 21 convergence convergence NOUN cana-1056 10 22 1 1 NUM cana-1056 10 23 . . PUNCT cana-1056 10 24 introduction introduction NOUN cana-1056 10 25 the the DET cana-1056 10 26 unconstrained unconstrained ADJ cana-1056 10 27 problem problem NOUN cana-1056 10 28 for for ADP cana-1056 10 29 an an DET cana-1056 10 30 optimization optimization NOUN cana-1056 10 31 defended defend VERB cana-1056 10 32 by by ADP cana-1056 10 33 : : PUNCT cana-1056 10 34 min min NOUN cana-1056 10 35 π‘“βŒ©π‘₯ π‘“βŒ©π‘₯ PROPN cana-1056 10 36 βŒͺ βŒͺ NOUN cana-1056 10 37 π‘₯ π‘₯ DET cana-1056 10 38 ∈ ∈ NOUN cana-1056 10 39 𝑅𝑛 𝑅𝑛 PROPN cana-1056 10 40 , , PUNCT cana-1056 10 41 ( ( PUNCT cana-1056 10 42 1 1 X cana-1056 10 43 ) ) PUNCT cana-1056 10 44 we we PRON cana-1056 10 45 have have VERB cana-1056 10 46 𝑓 𝑓 X cana-1056 10 47 : : PUNCT cana-1056 10 48 𝑅𝑛 𝑅𝑛 PROPN cana-1056 10 49 β†’ β†’ SYM cana-1056 10 50 𝑅 𝑅 PROPN cana-1056 10 51 is be AUX cana-1056 10 52 smooth smooth ADJ cana-1056 11 1 and and CCONJ cana-1056 11 2 it it PRON cana-1056 11 3 ’s ’ VERB cana-1056 11 4 βˆ‡π‘“ βˆ‡π‘“ NOUN cana-1056 11 5 is be AUX cana-1056 11 6 available available ADJ cana-1056 11 7 conjugate conjugate ADJ cana-1056 11 8 gradient(𝐢𝐺 gradient(𝐢𝐺 NOUN cana-1056 11 9 ) ) PUNCT cana-1056 11 10 method method NOUN cana-1056 11 11 for for ADP cana-1056 11 12 solving solve VERB cana-1056 11 13 ( ( PUNCT cana-1056 11 14 1)is 1)is NUM cana-1056 11 15 iterative iterative NOUN cana-1056 11 16 methods method NOUN cana-1056 11 17 of of ADP cana-1056 11 18 the the PRON cana-1056 11 19 from from ADP cana-1056 11 20 π‘₯π‘˜+1 π‘₯π‘˜+1 NOUN cana-1056 11 21 = = SYM cana-1056 11 22 π‘₯π‘˜ π‘₯π‘˜ X cana-1056 11 23 + + CCONJ cana-1056 11 24 π›Όπ‘˜π‘‘π‘˜ π›Όπ‘˜π‘‘π‘˜ NOUN cana-1056 11 25 ( ( PUNCT cana-1056 11 26 2 2 NUM cana-1056 11 27 ) ) PUNCT cana-1056 11 28 where where SCONJ cana-1056 11 29 π›Όπ‘˜ π›Όπ‘˜ ADV cana-1056 11 30 > > X cana-1056 11 31 0 0 NUM cana-1056 11 32 is be AUX cana-1056 11 33 step step NOUN cana-1056 11 34 size size NOUN cana-1056 11 35 and and CCONJ cana-1056 11 36 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 11 37 is be AUX cana-1056 11 38 search search NOUN cana-1056 11 39 direction direction NOUN cana-1056 11 40 , , PUNCT cana-1056 11 41 the the DET cana-1056 11 42 π‘‘π‘˜ π‘‘π‘˜ NOUN cana-1056 11 43 is be AUX cana-1056 11 44 recursively recursively ADV cana-1056 11 45 known know VERB cana-1056 11 46 as as ADP cana-1056 11 47 : : PUNCT cana-1056 11 48 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 11 49 = = PUNCT cana-1056 11 50 { { PUNCT cana-1056 11 51 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ X cana-1056 12 1 π‘“π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ NOUN cana-1056 12 2 π‘˜ π‘˜ X cana-1056 12 3 = = SYM cana-1056 12 4 1 1 NUM cana-1056 12 5 , , PUNCT cana-1056 12 6 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ PROPN cana-1056 13 1 + + CCONJ cana-1056 13 2 π›½π‘˜π‘‘π‘˜βˆ’1 π›½π‘˜π‘‘π‘˜βˆ’1 PROPN cana-1056 13 3 π‘“π‘œπ‘Ÿ π‘“π‘œπ‘Ÿ ADV cana-1056 13 4 π‘˜ π‘˜ DET cana-1056 13 5 β‰₯ β‰₯ NOUN cana-1056 13 6 2 2 NUM cana-1056 13 7 , , PUNCT cana-1056 13 8 ( ( PUNCT cana-1056 13 9 3 3 X cana-1056 13 10 ) ) PUNCT cana-1056 13 11 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 13 12 means mean VERB cana-1056 13 13 βˆ‡π‘“βŒ©π‘₯ βˆ‡π‘“βŒ©π‘₯ ADJ cana-1056 13 14 βŒͺ βŒͺ NOUN cana-1056 13 15 and and CCONJ cana-1056 13 16 π›½π‘˜ π›½π‘˜ NOUN cana-1056 13 17 is be AUX cana-1056 13 18 a a DET cana-1056 13 19 parameter parameter NOUN cana-1056 13 20 , , PUNCT cana-1056 13 21 if if SCONJ cana-1056 13 22 π‘“βŒ©π‘₯ π‘“βŒ©π‘₯ NOUN cana-1056 13 23 βŒͺ βŒͺ NOUN cana-1056 13 24 is be AUX cana-1056 13 25 a a DET cana-1056 13 26 strictly strictly ADV cana-1056 13 27 convex convex ADJ cana-1056 13 28 quadratic quadratic ADJ cana-1056 13 29 function function NOUN cana-1056 13 30 and and CCONJ cana-1056 13 31 π›Όπ‘˜ π›Όπ‘˜ PRON cana-1056 13 32 is be AUX cana-1056 13 33 an an DET cana-1056 13 34 exact exact ADJ cana-1056 13 35 one one NUM cana-1056 13 36 - - PUNCT cana-1056 13 37 dimension dimension NOUN cana-1056 13 38 min min NOUN cana-1056 13 39 .(1)-(3 .(1)-(3 PUNCT cana-1056 13 40 ) ) PUNCT cana-1056 14 1 is be AUX cana-1056 14 2 knows know VERB cana-1056 14 3 ( ( PUNCT cana-1056 14 4 cg cg NOUN cana-1056 14 5 ) ) PUNCT cana-1056 14 6 method method NOUN cana-1056 14 7 , , PUNCT cana-1056 14 8 also also ADV cana-1056 14 9 , , PUNCT cana-1056 14 10 ( ( PUNCT cana-1056 14 11 1)-(2 1)-(2 NUM cana-1056 14 12 ) ) PUNCT cana-1056 14 13 is be AUX cana-1056 14 14 knows know VERB cana-1056 14 15 the the DET cana-1056 14 16 nonlinear nonlinear ADJ cana-1056 14 17 ( ( PUNCT cana-1056 14 18 cg cg NOUN cana-1056 14 19 ) ) PUNCT cana-1056 14 20 method method NOUN cana-1056 14 21 . . PUNCT cana-1056 15 1 there there PRON cana-1056 15 2 are be VERB cana-1056 15 3 different different ADJ cana-1056 15 4 general general ADJ cana-1056 15 5 unconstrained unconstrained ADJ cana-1056 15 6 optimization optimization NOUN cana-1056 15 7 problems problem NOUN cana-1056 15 8 , , PUNCT cana-1056 15 9 famous famous ADJ cana-1056 15 10 prescription prescription NOUN cana-1056 15 11 for for ADP cana-1056 15 12 𝛽 𝛽 NOUN cana-1056 15 13 are be AUX cana-1056 15 14 the the DET cana-1056 15 15 ( ( PUNCT cana-1056 15 16 ls ls PROPN cana-1056 15 17 ) ) PUNCT cana-1056 16 1 [ [ X cana-1056 16 2 1 1 NUM cana-1056 16 3 ] ] PUNCT cana-1056 16 4 . . PUNCT cana-1056 17 1 ( ( PUNCT cana-1056 17 2 pr pr NOUN cana-1056 17 3 ) ) PUNCT cana-1056 18 1 [ [ X cana-1056 18 2 2 2 X cana-1056 18 3 ] ] PUNCT cana-1056 18 4 and and CCONJ cana-1056 18 5 ( ( PUNCT cana-1056 18 6 hs hs X cana-1056 18 7 ) ) PUNCT cana-1056 19 1 [ [ X cana-1056 19 2 3 3 X cana-1056 19 3 ] ] PUNCT cana-1056 19 4 which which PRON cana-1056 19 5 are be AUX cana-1056 19 6 as∢ as∢ VERB cana-1056 19 7 Ξ²k Ξ²k ADP cana-1056 19 8 ls ls PROPN cana-1056 19 9 = = PUNCT cana-1056 19 10 gk+1 gk+1 NOUN cana-1056 19 11 t t NOUN cana-1056 19 12 yk yk PROPN cana-1056 20 1 dk dk PROPN cana-1056 20 2 tgk tgk PROPN cana-1056 20 3 ( ( PUNCT cana-1056 20 4 4 4 NUM cana-1056 20 5 ) ) PUNCT cana-1056 20 6 Ξ²k Ξ²k ADP cana-1056 20 7 pr pr NOUN cana-1056 20 8 = = PUNCT cana-1056 20 9 gk gk PROPN cana-1056 20 10 t t PROPN cana-1056 20 11 ykβˆ’1 ykβˆ’1 PROPN cana-1056 20 12 β€–gkβˆ’1β€–2 β€–gkβˆ’1β€–2 NOUN cana-1056 20 13 ( ( PUNCT cana-1056 20 14 5 5 NUM cana-1056 20 15 ) ) PUNCT cana-1056 20 16 communications communication NOUN cana-1056 20 17 on on ADP cana-1056 20 18 applied apply VERB cana-1056 20 19 nonlinear nonlinear ADJ cana-1056 20 20 analysis analysis NOUN cana-1056 20 21 issn issn NOUN cana-1056 20 22 : : PUNCT cana-1056 20 23 1074 1074 NUM cana-1056 20 24 - - PUNCT cana-1056 20 25 133x 133x NUM cana-1056 20 26 vol vol NOUN cana-1056 20 27 31 31 NUM cana-1056 20 28 no no NOUN cana-1056 20 29 . . PUNCT cana-1056 21 1 5s 5s NUM cana-1056 21 2 ( ( PUNCT cana-1056 21 3 2024 2024 NUM cana-1056 21 4 ) ) PUNCT cana-1056 21 5 373 373 NUM cana-1056 21 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 21 7 Ξ²k Ξ²k ADP cana-1056 21 8 hs hs PROPN cana-1056 21 9 = = PROPN cana-1056 21 10 gk gk PROPN cana-1056 21 11 tykβˆ’1 tykβˆ’1 PROPN cana-1056 21 12 dkβˆ’1 dkβˆ’1 PROPN cana-1056 21 13 t t X cana-1056 21 14 ykβˆ’1 ykβˆ’1 NOUN cana-1056 21 15 ( ( PUNCT cana-1056 21 16 6 6 NUM cana-1056 21 17 ) ) PUNCT cana-1056 21 18 to to PART cana-1056 21 19 prove prove VERB cana-1056 21 20 the the DET cana-1056 21 21 convergence convergence NOUN cana-1056 21 22 of of ADP cana-1056 21 23 this this DET cana-1056 21 24 approach approach NOUN cana-1056 21 25 , , PUNCT cana-1056 21 26 it it PRON cana-1056 21 27 is be AUX cana-1056 21 28 often often ADV cana-1056 21 29 needed need VERB cana-1056 21 30 that that SCONJ cana-1056 21 31 the the DET cana-1056 21 32 step step NOUN cana-1056 21 33 - - PUNCT cana-1056 21 34 size size NOUN cana-1056 21 35 Ξ±_k Ξ±_k PRON cana-1056 21 36 satisfies satisfy VERB cana-1056 21 37 the the DET cana-1056 21 38 strong strong ADJ cana-1056 21 39 wolfe wolfe PROPN cana-1056 21 40 condition condition NOUN cana-1056 21 41 , , PUNCT cana-1056 21 42 where where SCONJ cana-1056 21 43 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 21 44 is be AUX cana-1056 21 45 defined define VERB cana-1056 21 46 as as ADP cana-1056 21 47 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 21 48 minus minus ADP cana-1056 21 49 π‘”π‘˜βˆ’1 π‘”π‘˜βˆ’1 NOUN cana-1056 21 50 , , PUNCT cana-1056 21 51 and and CCONJ cana-1056 21 52 β€–. β€–. PROPN cana-1056 21 53 β€– β€– PROPN cana-1056 21 54 represents represent VERB cana-1056 21 55 the the DET cana-1056 21 56 euclidean euclidean ADJ cana-1056 21 57 norm norm NOUN cana-1056 21 58 . . PUNCT cana-1056 22 1 f(xk f(xk X cana-1056 22 2 ) ) PUNCT cana-1056 22 3 βˆ’ βˆ’ ADP cana-1056 22 4 f(xk f(xk PROPN cana-1056 22 5 + + NUM cana-1056 22 6 Ξ±kdk Ξ±kdk NOUN cana-1056 22 7 ) ) PUNCT cana-1056 22 8 β‰₯ β‰₯ NOUN cana-1056 22 9 δαkgk δαkgk NOUN cana-1056 22 10 tdk tdk NOUN cana-1056 23 1 [ [ X cana-1056 23 2 4 4 NUM cana-1056 23 3 ] ] X cana-1056 23 4 ( ( PUNCT cana-1056 23 5 7 7 X cana-1056 23 6 ) ) PUNCT cana-1056 23 7 |g(xk |g(xk PROPN cana-1056 23 8 + + SYM cana-1056 23 9 Ξ±kdk)dk|t Ξ±kdk)dk|t PROPN cana-1056 23 10 ≀ ≀ PROPN cana-1056 23 11 βˆ’Οƒdk βˆ’Οƒdk NOUN cana-1056 23 12 tdk tdk NOUN cana-1056 24 1 [ [ X cana-1056 24 2 4 4 NUM cana-1056 24 3 ] ] X cana-1056 24 4 ( ( PUNCT cana-1056 24 5 8) 8) NUM cana-1056 24 6 where where SCONJ cana-1056 24 7 0 0 NUM cana-1056 24 8 < < X cana-1056 24 9 Ξ΄ Ξ΄ X cana-1056 24 10 < < X cana-1056 24 11 0.5 0.5 NUM cana-1056 24 12 < < X cana-1056 24 13 Οƒ Οƒ X cana-1056 24 14 < < X cana-1056 24 15 1 1 NUM cana-1056 24 16 each each DET cana-1056 24 17 method method NOUN cana-1056 24 18 comes come VERB cana-1056 24 19 with with ADP cana-1056 24 20 its its PRON cana-1056 24 21 own own ADJ cana-1056 24 22 advantages advantage NOUN cana-1056 24 23 and and CCONJ cana-1056 24 24 disadvantages disadvantage NOUN cana-1056 24 25 . . PUNCT cana-1056 25 1 see[5 see[5 VERB cana-1056 25 2 ] ] PUNCT cana-1056 25 3 , , PUNCT cana-1056 25 4 [ [ X cana-1056 25 5 3 3 X cana-1056 25 6 ] ] PUNCT cana-1056 25 7 the the DET cana-1056 25 8 polak polak NOUN cana-1056 25 9 - - PUNCT cana-1056 25 10 ribiere ribiere NOUN cana-1056 25 11 and and CCONJ cana-1056 25 12 hestenes hestene NOUN cana-1056 25 13 - - PUNCT cana-1056 25 14 stiefel stiefel NOUN cana-1056 25 15 ( ( PUNCT cana-1056 25 16 hs hs NOUN cana-1056 25 17 ) ) PUNCT cana-1056 25 18 methods method NOUN cana-1056 25 19 have have VERB cana-1056 25 20 comparable comparable ADJ cana-1056 25 21 theoretical theoretical ADJ cana-1056 25 22 properties property NOUN cana-1056 25 23 . . PUNCT cana-1056 26 1 both both PRON cana-1056 26 2 of of ADP cana-1056 26 3 these these DET cana-1056 26 4 methods method NOUN cana-1056 26 5 are be AUX cana-1056 26 6 favored favor VERB cana-1056 26 7 over over ADP cana-1056 26 8 the the DET cana-1056 26 9 liu liu PROPN cana-1056 26 10 - - PUNCT cana-1056 26 11 storey storey NOUN cana-1056 26 12 ( ( PUNCT cana-1056 26 13 ls ls PROPN cana-1056 26 14 ) ) PUNCT cana-1056 26 15 method method NOUN cana-1056 26 16 in in ADP cana-1056 26 17 terms term NOUN cana-1056 26 18 of of ADP cana-1056 26 19 numerical numerical ADJ cana-1056 26 20 performance performance NOUN cana-1056 26 21 . . PUNCT cana-1056 27 1 this this PRON cana-1056 27 2 is be AUX cana-1056 27 3 because because SCONJ cana-1056 27 4 they they PRON cana-1056 27 5 both both PRON cana-1056 27 6 restart restart VERB cana-1056 27 7 after after ADP cana-1056 27 8 encountering encounter VERB cana-1056 27 9 a a DET cana-1056 27 10 bad bad ADJ cana-1056 27 11 direction direction NOUN cana-1056 27 12 . . PUNCT cana-1056 28 1 however however ADV cana-1056 28 2 , , PUNCT cana-1056 28 3 the the DET cana-1056 28 4 yabe yabe NOUN cana-1056 28 5 - - PUNCT cana-1056 28 6 takano takano PROPN cana-1056 28 7 ( ( PUNCT cana-1056 28 8 yt yt NOUN cana-1056 28 9 ) ) PUNCT cana-1056 28 10 method method NOUN cana-1056 28 11 , , PUNCT cana-1056 28 12 derived derive VERB cana-1056 28 13 by by ADP cana-1056 28 14 zhang zhang PROPN cana-1056 28 15 et et PROPN cana-1056 28 16 al al PROPN cana-1056 28 17 in in ADP cana-1056 28 18 2004 2004 NUM cana-1056 28 19 , , PUNCT cana-1056 28 20 stands stand VERB cana-1056 28 21 out out ADP cana-1056 28 22 .[6 .[6 PROPN cana-1056 28 23 ] ] PUNCT cana-1056 28 24 and and CCONJ cana-1056 28 25 zhang[7]and zhang[7]and PROPN cana-1056 28 26 xu xu PUNCT cana-1056 29 1 [ [ X cana-1056 29 2 8 8 NUM cana-1056 29 3 ] ] PUNCT cana-1056 29 4 proposed propose VERB cana-1056 29 5 by by ADP cana-1056 29 6 yabe yabe PROPN cana-1056 29 7 - - PUNCT cana-1056 29 8 takano takano PROPN cana-1056 29 9 ( ( PUNCT cana-1056 29 10 yt)[9 yt)[9 PROPN cana-1056 29 11 ] ] X cana-1056 29 12 we we PRON cana-1056 29 13 propose propose VERB cana-1056 29 14 a a DET cana-1056 29 15 three three NUM cana-1056 29 16 news news NOUN cana-1056 29 17 formulas formula NOUN cana-1056 29 18 for for ADP cana-1056 29 19 π›½π‘˜ π›½π‘˜ NOUN cana-1056 29 20 𝑁1and 𝑁1and NOUN cana-1056 29 21 Ξ²k Ξ²k ADP cana-1056 29 22 n2and n2and ADV cana-1056 29 23 Ξ²k Ξ²k ADV cana-1056 29 24 n3 n3 ADJ cana-1056 29 25 by by ADP cana-1056 29 26 exploiting exploit VERB cana-1056 29 27 the the DET cana-1056 29 28 modified modified ADJ cana-1056 29 29 secant secant ADJ cana-1056 29 30 condition condition NOUN cana-1056 29 31 in in ADP cana-1056 29 32 this this DET cana-1056 29 33 paper paper NOUN cana-1056 29 34 is be AUX cana-1056 29 35 organized organize VERB cana-1056 29 36 as as SCONJ cana-1056 29 37 follows follow VERB cana-1056 29 38 , , PUNCT cana-1056 29 39 in in ADP cana-1056 29 40 section2 section2 NOUN cana-1056 29 41 we we PRON cana-1056 29 42 state state VERB cana-1056 29 43 a a DET cana-1056 29 44 conjugacy conjugacy ADJ cana-1056 29 45 condition condition NOUN cana-1056 29 46 and and CCONJ cana-1056 29 47 the the DET cana-1056 29 48 formulas formula NOUN cana-1056 29 49 in in ADP cana-1056 29 50 section3,the section3,the ADJ cana-1056 29 51 modified modified ADJ cana-1056 29 52 secant secant ADJ cana-1056 29 53 condition condition NOUN cana-1056 29 54 is be AUX cana-1056 29 55 described describe VERB cana-1056 29 56 in in ADP cana-1056 29 57 section section NOUN cana-1056 29 58 4 4 NUM cana-1056 29 59 , , PUNCT cana-1056 29 60 we we PRON cana-1056 29 61 suggest suggest VERB cana-1056 29 62 a a DET cana-1056 29 63 fresh fresh ADJ cana-1056 29 64 requirement requirement NOUN cana-1056 29 65 for for ADP cana-1056 29 66 conjugacy conjugacy NOUN cana-1056 29 67 and and CCONJ cana-1056 29 68 develop develop VERB cana-1056 29 69 novel novel ADJ cana-1056 29 70 equations equation NOUN cana-1056 29 71 for for ADP cana-1056 29 72 Ξ² Ξ² X cana-1056 29 73 . . PUNCT cana-1056 30 1 in in ADP cana-1056 30 2 section section NOUN cana-1056 30 3 5 5 NUM cana-1056 30 4 , , PUNCT cana-1056 30 5 we we PRON cana-1056 30 6 demonstrate demonstrate VERB cana-1056 30 7 the the DET cana-1056 30 8 worldwide worldwide ADJ cana-1056 30 9 convergence convergence NOUN cana-1056 30 10 of of ADP cana-1056 30 11 the the DET cana-1056 30 12 latest late ADJ cana-1056 30 13 conjugate conjugate ADJ cana-1056 30 14 gradient gradient NOUN cana-1056 30 15 techniques technique NOUN cana-1056 30 16 under under ADP cana-1056 30 17 specific specific ADJ cana-1056 30 18 assumptions assumption NOUN cana-1056 30 19 . . PUNCT cana-1056 31 1 section section NOUN cana-1056 31 2 6 6 NUM cana-1056 31 3 includes include VERB cana-1056 31 4 the the DET cana-1056 31 5 presentation presentation NOUN cana-1056 31 6 of of ADP cana-1056 31 7 a a DET cana-1056 31 8 few few ADJ cana-1056 31 9 numerical numerical ADJ cana-1056 31 10 trials trial NOUN cana-1056 31 11 . . PUNCT cana-1056 32 1 1.2 1.2 NUM cana-1056 32 2 yabe yabe NOUN cana-1056 32 3 - - PUNCT cana-1056 32 4 takano takano PROPN cana-1056 32 5 ( ( PUNCT cana-1056 32 6 yt yt NOUN cana-1056 32 7 ) ) PUNCT cana-1056 32 8 conjugate conjugate ADJ cana-1056 32 9 gradient gradient ADJ cana-1056 32 10 algorithm algorithm NOUN cana-1056 32 11 generates generate VERB cana-1056 32 12 a a DET cana-1056 32 13 direction direction NOUN cana-1056 32 14 search search NOUN cana-1056 32 15 such such ADJ cana-1056 32 16 that that SCONJ cana-1056 32 17 the the DET cana-1056 32 18 conjugacy conjugacy ADJ cana-1056 32 19 condition condition NOUN cana-1056 32 20 holds hold VERB cana-1056 32 21 , , PUNCT cana-1056 32 22 as as ADP cana-1056 32 23 , , PUNCT cana-1056 32 24 di di NOUN cana-1056 32 25 tqdj tqdj NOUN cana-1056 32 26 = = SYM cana-1056 32 27 0 0 NUM cana-1056 32 28 , , PUNCT cana-1056 32 29 βˆ€i βˆ€i NOUN cana-1056 32 30 β‰  β‰  PROPN cana-1056 32 31 j j PROPN cana-1056 32 32 ( ( PUNCT cana-1056 32 33 9 9 NUM cana-1056 32 34 ) ) PUNCT cana-1056 32 35 the the DET cana-1056 32 36 matrix matrix NOUN cana-1056 32 37 q q PUNCT cana-1056 32 38 is be AUX cana-1056 32 39 positive positive ADJ cana-1056 32 40 definite definite ADJ cana-1056 32 41 for for ADP cana-1056 32 42 the the DET cana-1056 32 43 quadratic quadratic ADJ cana-1056 32 44 objective objective ADJ cana-1056 32 45 function function NOUN cana-1056 32 46 . . PUNCT cana-1056 33 1 for for ADP cana-1056 33 2 general general ADJ cana-1056 33 3 nonlinear nonlinear ADJ cana-1056 33 4 functions function NOUN cana-1056 33 5 , , PUNCT cana-1056 33 6 the the DET cana-1056 33 7 mean mean ADJ cana-1056 33 8 value value NOUN cana-1056 33 9 theorem theorem NOUN cana-1056 33 10 ( ( PUNCT cana-1056 33 11 m.v.t m.v.t ADJ cana-1056 33 12 . . PUNCT cana-1056 33 13 ) ) PUNCT cana-1056 33 14 guarantees guarantee VERB cana-1056 33 15 the the DET cana-1056 33 16 existence existence NOUN cana-1056 33 17 of of ADP cana-1056 33 18 a a DET cana-1056 33 19 value value NOUN cana-1056 33 20 Ο„ Ο„ X cana-1056 33 21 in in ADP cana-1056 33 22 the the DET cana-1056 33 23 interval interval NOUN cana-1056 33 24 Ο„βˆˆ(0,1 Ο„βˆˆ(0,1 NOUN cana-1056 33 25 ) ) PUNCT cana-1056 33 26 such such ADJ cana-1056 33 27 that that SCONJ cana-1056 33 28 dk dk PROPN cana-1056 33 29 t t NOUN cana-1056 33 30 ykβˆ’1 ykβˆ’1 PROPN cana-1056 33 31 = = PUNCT cana-1056 33 32 Ξ±kβˆ’1π‘‘π‘˜ Ξ±kβˆ’1π‘‘π‘˜ NUM cana-1056 33 33 π‘‡βˆ‡2f(xkβˆ’1 π‘‡βˆ‡2f(xkβˆ’1 NOUN cana-1056 33 34 + + CCONJ cana-1056 33 35 ταkβˆ’1dkβˆ’1 ταkβˆ’1dkβˆ’1 NOUN cana-1056 33 36 ) ) PUNCT cana-1056 33 37 hence hence ADV cana-1056 33 38 , , PUNCT cana-1056 33 39 it it PRON cana-1056 33 40 is be AUX cana-1056 33 41 acceptable acceptable ADJ cana-1056 33 42 to to ADP cana-1056 33 43 substitute substitute NOUN cana-1056 33 44 ( ( PUNCT cana-1056 33 45 9 9 NUM cana-1056 33 46 ) ) PUNCT cana-1056 33 47 with with ADP cana-1056 33 48 the the DET cana-1056 33 49 subsequent subsequent ADJ cana-1056 33 50 condition condition NOUN cana-1056 33 51 : : PUNCT cana-1056 33 52 dk dk PRON cana-1056 33 53 tπ‘¦π‘˜βˆ’1 tπ‘¦π‘˜βˆ’1 PROPN cana-1056 33 54 = = SYM cana-1056 33 55 0 0 NUM cana-1056 33 56 ( ( PUNCT cana-1056 33 57 10 10 NUM cana-1056 33 58 ) ) PUNCT cana-1056 33 59 recently recently ADV cana-1056 33 60 , , PUNCT cana-1056 33 61 extension extension NOUN cana-1056 33 62 of of ADP cana-1056 33 63 the the DET cana-1056 33 64 cg cg NOUN cana-1056 33 65 has have AUX cana-1056 33 66 been be AUX cana-1056 33 67 studied study VERB cana-1056 33 68 yabe yabe NOUN cana-1056 33 69 - - PUNCT cana-1056 33 70 takano takano PROPN cana-1056 33 71 . . PUNCT cana-1056 34 1 [ [ X cana-1056 34 2 10 10 NUM cana-1056 34 3 ] ] PUNCT cana-1056 34 4 using use VERB cana-1056 34 5 the the DET cana-1056 34 6 secant secant ADJ cana-1056 34 7 condition condition NOUN cana-1056 34 8 of of ADP cana-1056 34 9 quasi quasi NOUN cana-1056 34 10 - - NOUN cana-1056 34 11 newton newton PROPN cana-1056 34 12 ( ( PUNCT cana-1056 34 13 qn qn NOUN cana-1056 34 14 ) ) PUNCT cana-1056 34 15 methods method NOUN cana-1056 34 16 , , PUNCT cana-1056 34 17 hkykβˆ’1 hkykβˆ’1 PROPN cana-1056 34 18 = = SYM cana-1056 34 19 skβˆ’1 skβˆ’1 ADJ cana-1056 34 20 . . PUNCT cana-1056 35 1 ( ( PUNCT cana-1056 35 2 11 11 NUM cana-1056 35 3 ) ) PUNCT cana-1056 35 4 where where SCONJ cana-1056 35 5 hk hk PROPN cana-1056 35 6 is be AUX cana-1056 35 7 an an DET cana-1056 35 8 inverse inverse NOUN cana-1056 35 9 approximate approximate NOUN cana-1056 35 10 for for ADP cana-1056 35 11 the the DET cana-1056 35 12 hessian hessian NOUN cana-1056 35 13 and and CCONJ cana-1056 35 14 π‘†π‘˜βˆ’1 π‘†π‘˜βˆ’1 PROPN cana-1056 35 15 = = SYM cana-1056 36 1 π‘₯π‘˜ π‘₯π‘˜ PROPN cana-1056 36 2 βˆ’ βˆ’ NOUN cana-1056 36 3 π‘₯π‘˜βˆ’1 π‘₯π‘˜βˆ’1 PROPN cana-1056 36 4 . . PUNCT cana-1056 37 1 for for ADP cana-1056 37 2 quasi_newton quasi_newton PROPN cana-1056 37 3 methods method NOUN cana-1056 37 4 , , PUNCT cana-1056 37 5 the the DET cana-1056 37 6 search search NOUN cana-1056 37 7 direction direction NOUN cana-1056 37 8 π‘‘π‘˜ π‘‘π‘˜ VERB cana-1056 37 9 can can AUX cana-1056 37 10 be be AUX cana-1056 37 11 calculated calculate VERB cana-1056 37 12 by by ADP cana-1056 37 13 : : PUNCT cana-1056 37 14 dk dk PROPN cana-1056 37 15 = = PUNCT cana-1056 37 16 βˆ’hkgk βˆ’hkgk X cana-1056 37 17 ( ( PUNCT cana-1056 37 18 12 12 NUM cana-1056 37 19 ) ) PUNCT cana-1056 37 20 communications communication NOUN cana-1056 37 21 on on ADP cana-1056 37 22 applied apply VERB cana-1056 37 23 nonlinear nonlinear ADJ cana-1056 37 24 analysis analysis NOUN cana-1056 37 25 issn issn NOUN cana-1056 37 26 : : PUNCT cana-1056 37 27 1074 1074 NUM cana-1056 37 28 - - PUNCT cana-1056 37 29 133x 133x NUM cana-1056 37 30 vol vol NOUN cana-1056 37 31 31 31 NUM cana-1056 37 32 no no NOUN cana-1056 37 33 . . PUNCT cana-1056 38 1 5s 5s NUM cana-1056 38 2 ( ( PUNCT cana-1056 38 3 2024 2024 NUM cana-1056 38 4 ) ) PUNCT cana-1056 38 5 374 374 NUM cana-1056 38 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 38 7 by by ADP cana-1056 38 8 ( ( PUNCT cana-1056 38 9 11 11 NUM cana-1056 38 10 ) ) PUNCT cana-1056 38 11 and and CCONJ cana-1056 38 12 ( ( PUNCT cana-1056 38 13 12 12 NUM cana-1056 38 14 ) ) PUNCT cana-1056 38 15 . . PUNCT cana-1056 39 1 we we PRON cana-1056 39 2 have have VERB cana-1056 39 3 that that SCONJ cana-1056 39 4 dk dk PRON cana-1056 39 5 tykβˆ’1 tykβˆ’1 PROPN cana-1056 39 6 = = PUNCT cana-1056 39 7 βˆ’(hkgk)tykβˆ’1 βˆ’(hkgk)tykβˆ’1 PROPN cana-1056 39 8 = = NOUN cana-1056 39 9 βˆ’gk βˆ’gk NOUN cana-1056 39 10 t(hkykβˆ’1 t(hkykβˆ’1 PROPN cana-1056 39 11 ) ) PUNCT cana-1056 40 1 = = SYM cana-1056 40 2 βˆ’gk βˆ’gk NOUN cana-1056 40 3 tskβˆ’1 tskβˆ’1 PROPN cana-1056 40 4 ( ( PUNCT cana-1056 40 5 13 13 NUM cana-1056 40 6 ) ) PUNCT cana-1056 40 7 by by ADP cana-1056 40 8 this this DET cana-1056 40 9 relation relation NOUN cana-1056 40 10 , , PUNCT cana-1056 40 11 dai dai PROPN cana-1056 40 12 and and CCONJ cana-1056 40 13 liao liao PROPN cana-1056 40 14 replaced replace VERB cana-1056 40 15 the the DET cana-1056 40 16 conjugacy conjugacy ADJ cana-1056 40 17 condition condition NOUN cana-1056 40 18 by by ADP cana-1056 40 19 the the DET cana-1056 40 20 condition condition NOUN cana-1056 40 21 π‘‘π‘˜ π‘‘π‘˜ ADP cana-1056 40 22 π‘‡π‘¦π‘˜βˆ’1 π‘‡π‘¦π‘˜βˆ’1 NOUN cana-1056 40 23 = = SYM cana-1056 40 24 βˆ’π‘‘π‘”π‘˜ βˆ’π‘‘π‘”π‘˜ NOUN cana-1056 40 25 π‘‡π‘ π‘˜βˆ’1 π‘‡π‘ π‘˜βˆ’1 PROPN cana-1056 40 26 ( ( PUNCT cana-1056 40 27 14 14 NUM cana-1056 40 28 ) ) PUNCT cana-1056 40 29 where where SCONJ cana-1056 40 30 𝑑 𝑑 PROPN cana-1056 40 31 β‰₯ β‰₯ X cana-1056 40 32 0 0 NUM cana-1056 40 33 is be AUX cana-1056 40 34 a a DET cana-1056 40 35 scalar scalar NOUN cana-1056 40 36 . . PUNCT cana-1056 41 1 in in ADP cana-1056 41 2 the the DET cana-1056 41 3 scenario scenario NOUN cana-1056 41 4 where where SCONJ cana-1056 41 5 t=0 t=0 PROPN cana-1056 41 6 , , PUNCT cana-1056 41 7 equation equation NOUN cana-1056 41 8 ( ( PUNCT cana-1056 41 9 11 11 NUM cana-1056 41 10 ) ) PUNCT cana-1056 41 11 simplifies simplifie NOUN cana-1056 41 12 to to ADP cana-1056 41 13 the the DET cana-1056 41 14 standard standard ADJ cana-1056 41 15 conjugacy conjugacy ADJ cana-1056 41 16 condition condition NOUN cana-1056 41 17 ( ( PUNCT cana-1056 41 18 10 10 NUM cana-1056 41 19 ) ) PUNCT cana-1056 41 20 . . PUNCT cana-1056 42 1 conversely conversely ADV cana-1056 42 2 , , PUNCT cana-1056 42 3 when when SCONJ cana-1056 42 4 t=1 t=1 NOUN cana-1056 42 5 , , PUNCT cana-1056 42 6 equation equation NOUN cana-1056 42 7 ( ( PUNCT cana-1056 42 8 11 11 NUM cana-1056 42 9 ) ) PUNCT cana-1056 42 10 becomes become VERB cana-1056 42 11 equivalent equivalent ADJ cana-1056 42 12 to to ADP cana-1056 42 13 ( ( PUNCT cana-1056 42 14 10 10 NUM cana-1056 42 15 ) ) PUNCT cana-1056 42 16 . . PUNCT cana-1056 43 1 in in ADP cana-1056 43 2 order order NOUN cana-1056 43 3 to to PART cana-1056 43 4 guarantee guarantee VERB cana-1056 43 5 that that SCONJ cana-1056 43 6 the the DET cana-1056 43 7 search search NOUN cana-1056 43 8 direction direction NOUN cana-1056 43 9 dk dk PROPN cana-1056 43 10 meets meet VERB cana-1056 43 11 this this DET cana-1056 43 12 requirement requirement NOUN cana-1056 43 13 , , PUNCT cana-1056 43 14 we we PRON cana-1056 43 15 can can AUX cana-1056 43 16 substitute substitute VERB cana-1056 43 17 equation equation NOUN cana-1056 43 18 ( ( PUNCT cana-1056 43 19 3 3 NUM cana-1056 43 20 ) ) PUNCT cana-1056 43 21 into into ADP cana-1056 43 22 ( ( PUNCT cana-1056 43 23 14 14 NUM cana-1056 43 24 ) ) PUNCT cana-1056 43 25 to to PART cana-1056 43 26 obtain obtain VERB cana-1056 43 27 : : PUNCT cana-1056 43 28 βˆ’gk βˆ’gk NOUN cana-1056 43 29 tykβˆ’1 tykβˆ’1 PROPN cana-1056 43 30 + + CCONJ cana-1056 43 31 Ξ²kdkβˆ’1 Ξ²kdkβˆ’1 PROPN cana-1056 43 32 t t NOUN cana-1056 43 33 ykβˆ’1 ykβˆ’1 NOUN cana-1056 43 34 = = PUNCT cana-1056 43 35 βˆ’tgk βˆ’tgk NOUN cana-1056 44 1 tskβˆ’1 tskβˆ’1 PROPN cana-1056 45 1 [ [ X cana-1056 45 2 10 10 NUM cana-1056 45 3 ] ] X cana-1056 45 4 ( ( PUNCT cana-1056 45 5 15 15 NUM cana-1056 45 6 ) ) PUNCT cana-1056 45 7 2.new 2.new ADJ cana-1056 45 8 formulas formula NOUN cana-1056 45 9 for for ADP cana-1056 45 10 𝛃𝐀 𝛃𝐀 ADP cana-1056 45 11 𝐍𝟏 𝐍𝟏 NOUN cana-1056 45 12 , , PUNCT cana-1056 45 13 𝛃𝐀 𝛃𝐀 ADP cana-1056 45 14 𝐍𝟐 𝐍𝟐 PROPN cana-1056 45 15 , , PUNCT cana-1056 45 16 𝛃𝐀 𝛃𝐀 ADP cana-1056 45 17 ππŸ‘ ππŸ‘ PROPN cana-1056 45 18 we we PRON cana-1056 45 19 are be AUX cana-1056 45 20 developed develop VERB cana-1056 45 21 a a DET cana-1056 45 22 new new ADJ cana-1056 45 23 conjugate conjugate ADJ cana-1056 45 24 gradient gradient NOUN cana-1056 45 25 ( ( PUNCT cana-1056 45 26 cg cg NOUN cana-1056 45 27 ) ) PUNCT cana-1056 45 28 method method NOUN cana-1056 45 29 in in ADP cana-1056 45 30 this this DET cana-1056 45 31 part part NOUN cana-1056 45 32 based base VERB cana-1056 45 33 on on ADP cana-1056 45 34 the the DET cana-1056 45 35 work work NOUN cana-1056 45 36 of of ADP cana-1056 45 37 yabetakano yabetakano NOUN cana-1056 46 1 [ [ X cana-1056 46 2 10 10 NUM cana-1056 46 3 ] ] PUNCT cana-1056 46 4 . . PUNCT cana-1056 47 1 to to PART cana-1056 47 2 achieve achieve VERB cana-1056 47 3 this this DET cana-1056 47 4 work work NOUN cana-1056 47 5 , , PUNCT cana-1056 47 6 we we PRON cana-1056 47 7 apply apply VERB cana-1056 47 8 a a DET cana-1056 47 9 modified modified ADJ cana-1056 47 10 secant secant ADJ cana-1056 47 11 condition condition NOUN cana-1056 47 12 ( ( PUNCT cana-1056 47 13 3.2 3.2 NUM cana-1056 47 14 ) ) PUNCT cana-1056 47 15 instead instead ADV cana-1056 47 16 of of ADP cana-1056 47 17 the the DET cana-1056 47 18 usual usual ADJ cana-1056 47 19 one one NUM cana-1056 47 20 ( ( PUNCT cana-1056 47 21 6 6 NUM cana-1056 47 22 ) ) PUNCT cana-1056 47 23 . . PUNCT cana-1056 48 1 let let VERB cana-1056 48 2 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 48 3 be be AUX cana-1056 48 4 defined define VERB cana-1056 48 5 with with ADP cana-1056 48 6 a a DET cana-1056 48 7 scalar scalar ADJ cana-1056 48 8 parameter parameter NOUN cana-1056 48 9 ρ ρ PROPN cana-1056 48 10 β‰₯ β‰₯ PROPN cana-1056 48 11 0 0 NUM cana-1056 48 12 : : PUNCT cana-1056 48 13 { { PUNCT cana-1056 48 14 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 48 15 = = SYM cana-1056 48 16 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 48 17 + + PROPN cana-1056 48 18 ρ ρ PROPN cana-1056 48 19 ( ( PUNCT cana-1056 48 20 πœƒπ‘˜βˆ’1 πœƒπ‘˜βˆ’1 PROPN cana-1056 48 21 π‘ π‘˜ π‘ π‘˜ NOUN cana-1056 48 22 π‘‡π‘’π‘˜βˆ’1 π‘‡π‘’π‘˜βˆ’1 PROPN cana-1056 48 23 ) ) PUNCT cana-1056 48 24 ΞΈkβˆ’1 ΞΈkβˆ’1 PROPN cana-1056 48 25 = = PUNCT cana-1056 48 26 6(fkβˆ’1 6(fkβˆ’1 PROPN cana-1056 48 27 βˆ’ βˆ’ PROPN cana-1056 48 28 fk fk INTJ cana-1056 48 29 ) ) PUNCT cana-1056 49 1 + + CCONJ cana-1056 49 2 3(gkβˆ’1 3(gkβˆ’1 NUM cana-1056 49 3 + + NUM cana-1056 49 4 gk)tskβˆ’1 gk)tskβˆ’1 NUM cana-1056 49 5 [ [ X cana-1056 49 6 11],[12 11],[12 NOUN cana-1056 49 7 ] ] X cana-1056 49 8 ( ( PUNCT cana-1056 49 9 16 16 NUM cana-1056 49 10 ) ) PUNCT cana-1056 49 11 building build VERB cana-1056 49 12 upon upon SCONJ cana-1056 49 13 the the DET cana-1056 49 14 same same ADJ cana-1056 49 15 reasoning reasoning NOUN cana-1056 49 16 as as ADP cana-1056 49 17 in in ADP cana-1056 49 18 part part NOUN cana-1056 49 19 2 2 NUM cana-1056 49 20 , , PUNCT cana-1056 49 21 we we PRON cana-1056 49 22 examine examine VERB cana-1056 49 23 the the DET cana-1056 49 24 adjusted adjusted ADJ cana-1056 49 25 secant secant ADJ cana-1056 49 26 condition condition NOUN cana-1056 49 27 involving involve VERB cana-1056 49 28 with with ADP cana-1056 49 29 zkβˆ’1 zkβˆ’1 PROPN cana-1056 49 30 hkzkβˆ’1 hkzkβˆ’1 PROPN cana-1056 49 31 = = SYM cana-1056 49 32 skβˆ’1 skβˆ’1 PROPN cana-1056 49 33 ( ( PUNCT cana-1056 49 34 17 17 NUM cana-1056 49 35 ) ) PUNCT cana-1056 49 36 when when SCONJ cana-1056 49 37 𝜌 𝜌 X cana-1056 49 38 = = SYM cana-1056 49 39 0 0 NUM cana-1056 49 40 and and CCONJ cana-1056 49 41 𝜌 𝜌 X cana-1056 49 42 = = SYM cana-1056 50 1 1,[6 1,[6 NUM cana-1056 50 2 ] ] PUNCT cana-1056 50 3 this this DET cana-1056 50 4 situation situation NOUN cana-1056 50 5 aligns align VERB cana-1056 50 6 with with ADP cana-1056 50 7 the the DET cana-1056 50 8 typical typical ADJ cana-1056 50 9 secant secant ADJ cana-1056 50 10 condition condition NOUN cana-1056 50 11 ( ( PUNCT cana-1056 50 12 6 6 NUM cana-1056 50 13 ) ) PUNCT cana-1056 50 14 and and CCONJ cana-1056 50 15 the the DET cana-1056 50 16 revised revise VERB cana-1056 50 17 secant secant ADJ cana-1056 50 18 condition condition NOUN cana-1056 50 19 ( ( PUNCT cana-1056 50 20 3.2 3.2 NUM cana-1056 50 21 ) ) PUNCT cana-1056 50 22 individually individually ADV cana-1056 50 23 . . PUNCT cana-1056 51 1 it it PRON cana-1056 51 2 follows follow VERB cana-1056 51 3 from from ADP cana-1056 51 4 ( ( PUNCT cana-1056 51 5 7 7 NUM cana-1056 51 6 ) ) PUNCT cana-1056 51 7 and and CCONJ cana-1056 51 8 ( ( PUNCT cana-1056 51 9 12 12 NUM cana-1056 51 10 ) ) PUNCT cana-1056 51 11 that that PRON cana-1056 51 12 : : PUNCT cana-1056 51 13 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 51 14 π‘‡π‘§π‘˜βˆ’1 π‘‡π‘§π‘˜βˆ’1 X cana-1056 51 15 = = PUNCT cana-1056 51 16 βˆ’(π»π‘˜π‘”π‘˜)π‘‡π‘§π‘˜βˆ’1 βˆ’(π»π‘˜π‘”π‘˜)π‘‡π‘§π‘˜βˆ’1 PROPN cana-1056 51 17 = = SYM cana-1056 51 18 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ PROPN cana-1056 51 19 𝑇(π»π‘˜π‘§π‘˜βˆ’1 𝑇(π»π‘˜π‘§π‘˜βˆ’1 PROPN cana-1056 51 20 ) ) PUNCT cana-1056 51 21 = = SYM cana-1056 52 1 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ X cana-1056 52 2 π‘‡π‘ π‘˜βˆ’1 π‘‡π‘ π‘˜βˆ’1 PROPN cana-1056 52 3 ( ( PUNCT cana-1056 52 4 18 18 NUM cana-1056 52 5 ) ) PUNCT cana-1056 52 6 considering consider VERB cana-1056 52 7 this this DET cana-1056 52 8 relationship relationship NOUN cana-1056 52 9 , , PUNCT cana-1056 52 10 we we PRON cana-1056 52 11 substitute substitute VERB cana-1056 52 12 the the DET cana-1056 52 13 conjugacy conjugacy PROPN cana-1056 52 14 requirement requirement NOUN cana-1056 52 15 with with ADP cana-1056 52 16 the the DET cana-1056 52 17 updated update VERB cana-1056 52 18 condition condition NOUN cana-1056 52 19 . . PUNCT cana-1056 53 1 : : PUNCT cana-1056 53 2 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 53 3 π‘‡π‘§π‘˜βˆ’1 π‘‡π‘§π‘˜βˆ’1 PUNCT cana-1056 53 4 = = SYM cana-1056 53 5 βˆ’π‘‘π‘”π‘˜ βˆ’π‘‘π‘”π‘˜ X cana-1056 53 6 π‘‡π‘ π‘˜βˆ’1 π‘‡π‘ π‘˜βˆ’1 PROPN cana-1056 53 7 , , PUNCT cana-1056 53 8 ( ( PUNCT cana-1056 53 9 19 19 NUM cana-1056 53 10 ) ) PUNCT cana-1056 53 11 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 53 12 = = PUNCT cana-1056 53 13 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ PROPN cana-1056 54 1 + + CCONJ cana-1056 54 2 π›½π‘˜π‘‘π‘˜βˆ’1 π›½π‘˜π‘‘π‘˜βˆ’1 PROPN cana-1056 54 3 π»πΎπ‘§π‘˜βˆ’1 π»πΎπ‘§π‘˜βˆ’1 X cana-1056 55 1 = = PRON cana-1056 55 2 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 55 3 π»πΎπ‘¦π‘˜βˆ’1 π»πΎπ‘¦π‘˜βˆ’1 PROPN cana-1056 56 1 = = PUNCT cana-1056 56 2 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 56 3 ( ( PUNCT cana-1056 56 4 20 20 NUM cana-1056 56 5 ) ) PUNCT cana-1056 56 6 π‘‘π‘˜π‘§π‘˜ π‘‘π‘˜π‘§π‘˜ NOUN cana-1056 56 7 = = SYM cana-1056 56 8 βˆ’π‘”π‘˜π‘ π‘˜βˆ’1 βˆ’π‘”π‘˜π‘ π‘˜βˆ’1 X cana-1056 56 9 π‘‘π‘˜π‘§π‘˜ π‘‘π‘˜π‘§π‘˜ NOUN cana-1056 56 10 = = SYM cana-1056 56 11 βˆ’π‘‘π‘”π‘˜π‘ π‘˜βˆ’1 βˆ’π‘‘π‘”π‘˜π‘ π‘˜βˆ’1 PROPN cana-1056 56 12 while while SCONJ cana-1056 56 13 π‘§π‘˜ π‘§π‘˜ PRON cana-1056 56 14 = = SYM cana-1056 56 15 π‘¦π‘˜ π‘¦π‘˜ PROPN cana-1056 56 16 + + CCONJ cana-1056 56 17 πœƒπ‘˜ πœƒπ‘˜ VERB cana-1056 56 18 β€–π‘ π‘˜β€–2 β€–π‘ π‘˜β€–2 PROPN cana-1056 56 19 π‘ π‘˜ π‘ π‘˜ NOUN cana-1056 56 20 ( ( PUNCT cana-1056 56 21 21 21 NUM cana-1056 56 22 ) ) PUNCT cana-1056 56 23 πœƒπ‘˜ πœƒπ‘˜ NOUN cana-1056 57 1 = = SYM cana-1056 57 2 6(π‘“π‘˜ 6(π‘“π‘˜ PROPN cana-1056 57 3 βˆ’ βˆ’ PROPN cana-1056 57 4 π‘“π‘˜βˆ’1 π‘“π‘˜βˆ’1 PROPN cana-1056 57 5 ) ) PUNCT cana-1056 58 1 + + NUM cana-1056 58 2 3(π‘”π‘˜ 3(π‘”π‘˜ NUM cana-1056 58 3 βˆ’ βˆ’ PROPN cana-1056 59 1 π‘”π‘˜βˆ’1)π‘ π‘˜ π‘”π‘˜βˆ’1)π‘ π‘˜ PROPN cana-1056 59 2 for for ADP cana-1056 59 3 𝑑 𝑑 PROPN cana-1056 59 4 β‰₯ β‰₯ NOUN cana-1056 59 5 0 0 NUM cana-1056 59 6 ( ( PUNCT cana-1056 59 7 22 22 NUM cana-1056 59 8 ) ) PUNCT cana-1056 59 9 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 59 10 = = SYM cana-1056 59 11 βˆ’π»π‘˜π‘”π‘˜ βˆ’π»π‘˜π‘”π‘˜ X cana-1056 59 12 ( ( PUNCT cana-1056 59 13 23 23 NUM cana-1056 59 14 ) ) PUNCT cana-1056 59 15 communications communication NOUN cana-1056 59 16 on on ADP cana-1056 59 17 applied apply VERB cana-1056 59 18 nonlinear nonlinear ADJ cana-1056 59 19 analysis analysis NOUN cana-1056 59 20 issn issn NOUN cana-1056 59 21 : : PUNCT cana-1056 59 22 1074 1074 NUM cana-1056 59 23 - - PUNCT cana-1056 59 24 133x 133x NUM cana-1056 59 25 vol vol NOUN cana-1056 59 26 31 31 NUM cana-1056 59 27 no no NOUN cana-1056 59 28 . . PUNCT cana-1056 60 1 5s 5s NUM cana-1056 60 2 ( ( PUNCT cana-1056 60 3 2024 2024 NUM cana-1056 60 4 ) ) PUNCT cana-1056 60 5 375 375 NUM cana-1056 60 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 60 7 π‘‘π‘˜ π‘‘π‘˜ ADP cana-1056 60 8 π‘‡π‘¦π‘˜ π‘‡π‘¦π‘˜ PROPN cana-1056 60 9 = = SYM cana-1056 60 10 0 0 NUM cana-1056 60 11 ( ( PUNCT cana-1056 60 12 perry perry PROPN cana-1056 60 13 ) ) PUNCT cana-1056 60 14 , , PUNCT cana-1056 60 15 this this DET cana-1056 60 16 condition condition NOUN cana-1056 60 17 is be AUX cana-1056 60 18 true true ADJ cana-1056 60 19 for for ADP cana-1056 60 20 all all DET cana-1056 60 21 liner liner NOUN cana-1056 60 22 functions function NOUN cana-1056 60 23 π‘‘π‘˜π‘¦π‘˜ π‘‘π‘˜π‘¦π‘˜ NOUN cana-1056 60 24 = = SYM cana-1056 60 25 βˆ’π»π‘˜π‘”π‘˜π‘¦π‘˜ βˆ’π»π‘˜π‘”π‘˜π‘¦π‘˜ NOUN cana-1056 60 26 ( ( PUNCT cana-1056 60 27 24 24 NUM cana-1056 60 28 ) ) PUNCT cana-1056 60 29 π‘‘π‘˜ π‘‘π‘˜ ADP cana-1056 60 30 π‘‡π‘¦π‘˜ π‘‡π‘¦π‘˜ PROPN cana-1056 60 31 = = SYM cana-1056 60 32 βˆ’π‘”π‘˜βˆ’1 βˆ’π‘”π‘˜βˆ’1 PROPN cana-1056 60 33 𝑇 𝑇 PROPN cana-1056 60 34 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 60 35 , , PUNCT cana-1056 60 36 this this DET cana-1056 60 37 condition condition NOUN cana-1056 60 38 is be AUX cana-1056 60 39 true true ADJ cana-1056 60 40 for for ADP cana-1056 60 41 all all DET cana-1056 60 42 nonlinear nonlinear ADJ cana-1056 60 43 functions function NOUN cana-1056 60 44 π‘‘π‘˜π‘¦π‘˜ π‘‘π‘˜π‘¦π‘˜ NOUN cana-1056 60 45 = = SYM cana-1056 60 46 βˆ’π‘‘π‘”π‘˜π‘ π‘˜βˆ’1 βˆ’π‘‘π‘”π‘˜π‘ π‘˜βˆ’1 PROPN cana-1056 60 47 ( ( PUNCT cana-1056 60 48 25 25 NUM cana-1056 60 49 ) ) PUNCT cana-1056 60 50 multiply multiply ADP cana-1056 60 51 the the DET cana-1056 60 52 equation(25)by equation(25)by NOUN cana-1056 60 53 𝑧𝐾we 𝑧𝐾we PROPN cana-1056 60 54 get get VERB cana-1056 60 55 π‘‘π‘˜π‘§π‘˜ π‘‘π‘˜π‘§π‘˜ ADJ cana-1056 60 56 = = PUNCT cana-1056 60 57 βˆ’π‘”π‘˜π‘§π‘˜ βˆ’π‘”π‘˜π‘§π‘˜ NOUN cana-1056 60 58 + + CCONJ cana-1056 60 59 π›½π‘˜π‘‘π‘˜βˆ’1π‘§π‘˜ π›½π‘˜π‘‘π‘˜βˆ’1π‘§π‘˜ PROPN cana-1056 60 60 ( ( PUNCT cana-1056 60 61 26 26 NUM cana-1056 60 62 ) ) PUNCT cana-1056 60 63 βˆ’π‘‘π‘”π‘˜ βˆ’π‘‘π‘”π‘˜ NOUN cana-1056 61 1 π‘‡π‘ π‘˜ π‘‡π‘ π‘˜ NOUN cana-1056 61 2 = = SYM cana-1056 61 3 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ X cana-1056 62 1 π‘‡π‘§π‘˜ π‘‡π‘§π‘˜ PROPN cana-1056 62 2 + + CCONJ cana-1056 62 3 π›½π‘˜π‘‘π‘˜βˆ’1 π›½π‘˜π‘‘π‘˜βˆ’1 PROPN cana-1056 62 4 𝑇 𝑇 PROPN cana-1056 62 5 π‘§π‘˜ π‘§π‘˜ X cana-1056 62 6 ( ( PUNCT cana-1056 62 7 27 27 NUM cana-1056 62 8 ) ) PUNCT cana-1056 62 9 βˆ’π‘‘π‘”π‘˜ βˆ’π‘‘π‘”π‘˜ NOUN cana-1056 63 1 π‘‡π‘ π‘˜ π‘‡π‘ π‘˜ NOUN cana-1056 63 2 = = SYM cana-1056 63 3 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ X cana-1056 64 1 π‘‡π‘§π‘˜ π‘‡π‘§π‘˜ PROPN cana-1056 64 2 + + CCONJ cana-1056 64 3 π›½π‘˜π‘‘π‘˜βˆ’1 π›½π‘˜π‘‘π‘˜βˆ’1 PROPN cana-1056 64 4 𝑇 𝑇 PROPN cana-1056 64 5 π‘¦π‘˜ π‘¦π‘˜ NOUN cana-1056 64 6 ( ( PUNCT cana-1056 64 7 28 28 NUM cana-1056 64 8 ) ) PUNCT cana-1056 64 9 ( ( PUNCT cana-1056 64 10 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 64 11 π‘‡π‘§π‘˜ π‘‡π‘§π‘˜ PROPN cana-1056 64 12 βˆ’ βˆ’ PROPN cana-1056 64 13 π‘‘π‘”π‘˜ π‘‘π‘”π‘˜ NOUN cana-1056 64 14 π‘‡π‘ π‘˜)= π‘‡π‘ π‘˜)= ADJ cana-1056 64 15 π›½π‘˜π‘‘π‘˜ π›½π‘˜π‘‘π‘˜ NOUN cana-1056 64 16 π‘‡π‘¦π‘˜βˆ’1 π‘‡π‘¦π‘˜βˆ’1 PUNCT cana-1056 64 17 ( ( PUNCT cana-1056 64 18 29 29 NUM cana-1056 64 19 ) ) PUNCT cana-1056 64 20 π›½π‘˜ π›½π‘˜ ADP cana-1056 64 21 𝑁1 𝑁1 PROPN cana-1056 64 22 = = PUNCT cana-1056 64 23 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 64 24 𝑇(π‘§π‘˜βˆ’π‘‘π‘ π‘˜ 𝑇(π‘§π‘˜βˆ’π‘‘π‘ π‘˜ NOUN cana-1056 64 25 ) ) PUNCT cana-1056 64 26 π‘‘π‘˜ π‘‘π‘˜ ADP cana-1056 64 27 π‘‡π‘¦π‘˜βˆ’1 π‘‡π‘¦π‘˜βˆ’1 PROPN cana-1056 64 28 ( ( PUNCT cana-1056 64 29 30 30 NUM cana-1056 64 30 ) ) PUNCT cana-1056 64 31 in in ADP cana-1056 64 32 the the DET cana-1056 64 33 next next ADJ cana-1056 64 34 section section NOUN cana-1056 64 35 , , PUNCT cana-1056 64 36 we we PRON cana-1056 64 37 proved prove VERB cana-1056 64 38 the the DET cana-1056 64 39 global global ADJ cana-1056 64 40 convergence convergence NOUN cana-1056 64 41 of of ADP cana-1056 64 42 the the DET cana-1056 64 43 new new ADJ cana-1056 64 44 methods method NOUN cana-1056 64 45 ( ( PUNCT cana-1056 64 46 30 30 NUM cana-1056 64 47 ) ) PUNCT cana-1056 64 48 , , PUNCT cana-1056 64 49 following follow VERB cana-1056 64 50 the the DET cana-1056 64 51 liostory liostory ADJ cana-1056 64 52 methods method NOUN cana-1056 64 53 , , PUNCT cana-1056 64 54 we we PRON cana-1056 64 55 are be AUX cana-1056 64 56 get get VERB cana-1056 64 57 by by ADP cana-1056 64 58 using use VERB cana-1056 64 59 ( ( PUNCT cana-1056 64 60 30 30 NUM cana-1056 64 61 ) ) PUNCT cana-1056 64 62 π›½π‘˜ π›½π‘˜ ADP cana-1056 64 63 𝑁1 𝑁1 PROPN cana-1056 64 64 = = SYM cana-1056 64 65 π‘€π‘Žπ‘₯ π‘€π‘Žπ‘₯ PROPN cana-1056 64 66 { { PUNCT cana-1056 64 67 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 64 68 π‘‡π‘§π‘˜ π‘‡π‘§π‘˜ PROPN cana-1056 64 69 π‘‘π‘˜βˆ’1 π‘‘π‘˜βˆ’1 PROPN cana-1056 64 70 𝑇 𝑇 PROPN cana-1056 64 71 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 64 72 , , PUNCT cana-1056 64 73 0 0 NUM cana-1056 64 74 } } PUNCT cana-1056 64 75 βˆ’ βˆ’ PROPN cana-1056 64 76 𝑑 𝑑 NOUN cana-1056 64 77 { { PUNCT cana-1056 64 78 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 64 79 𝑇 𝑇 PROPN cana-1056 64 80 π‘ π‘˜ π‘ π‘˜ NOUN cana-1056 64 81 π‘‘π‘˜ π‘‘π‘˜ ADP cana-1056 64 82 𝑇 𝑇 PROPN cana-1056 64 83 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 64 84 , , PUNCT cana-1056 64 85 0 0 NUM cana-1056 64 86 } } PUNCT cana-1056 64 87 ( ( PUNCT cana-1056 64 88 31 31 NUM cana-1056 64 89 ) ) PUNCT cana-1056 64 90 this this DET cana-1056 64 91 case case NOUN cana-1056 64 92 , , PUNCT cana-1056 64 93 if if SCONJ cana-1056 64 94 ( ( PUNCT cana-1056 64 95 els el NOUN cana-1056 64 96 ) ) PUNCT cana-1056 64 97 then then ADV cana-1056 64 98 we we PRON cana-1056 64 99 have have AUX cana-1056 64 100 πœƒπ‘˜βˆ’1 πœƒπ‘˜βˆ’1 NOUN cana-1056 64 101 = = SYM cana-1056 64 102 0 0 NUM cana-1056 64 103 , , PUNCT cana-1056 64 104 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 64 105 = = PRON cana-1056 64 106 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 64 107 the the DET cana-1056 64 108 new new ADJ cana-1056 64 109 parameters parameter NOUN cana-1056 64 110 becomeπ‘”π‘˜ becomeπ‘”π‘˜ VERB cana-1056 64 111 π‘‡π‘¦π‘˜βˆ’1/π‘‘π‘˜ π‘‡π‘¦π‘˜βˆ’1/π‘‘π‘˜ PROPN cana-1056 64 112 π‘‡π‘¦π‘˜βˆ’1 π‘‡π‘¦π‘˜βˆ’1 PROPN cana-1056 64 113 . . PUNCT cana-1056 65 1 thus thus ADV cana-1056 65 2 , , PUNCT cana-1056 65 3 our our PRON cana-1056 65 4 equation equation NOUN cana-1056 65 5 ( ( PUNCT cana-1056 65 6 30 30 NUM cana-1056 65 7 ) ) PUNCT cana-1056 65 8 simplifies simplifie NOUN cana-1056 65 9 to to ADP cana-1056 65 10 the the DET cana-1056 65 11 hestenes hestene NOUN cana-1056 65 12 - - PUNCT cana-1056 65 13 stiefel stiefel NOUN cana-1056 65 14 formula formula NOUN cana-1056 65 15 when when SCONJ cana-1056 65 16 considering consider VERB cana-1056 65 17 linear linear ADJ cana-1056 65 18 conjugate conjugate ADJ cana-1056 65 19 gradient gradient NOUN cana-1056 65 20 techniques technique NOUN cana-1056 65 21 . . PUNCT cana-1056 65 22 . . PUNCT cana-1056 66 1 similarly similarly ADV cana-1056 66 2 we we PRON cana-1056 66 3 have have AUX cana-1056 66 4 derive derive ADJ cana-1056 66 5 , , PUNCT cana-1056 66 6 Ξ²k Ξ²k NOUN cana-1056 66 7 n2 n2 ADJ cana-1056 66 8 , , PUNCT cana-1056 66 9 Ξ²k Ξ²k ADP cana-1056 66 10 n3 n3 NOUN cana-1056 66 11 Ξ²k Ξ²k NOUN cana-1056 66 12 n2 n2 NOUN cana-1056 66 13 = = PUNCT cana-1056 66 14 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 66 15 𝑇(π‘§π‘˜βˆ’π‘‘π‘ π‘˜ 𝑇(π‘§π‘˜βˆ’π‘‘π‘ π‘˜ NOUN cana-1056 66 16 ) ) PUNCT cana-1056 66 17 β€–π‘”π‘˜βˆ’1β€–2 β€–π‘”π‘˜βˆ’1β€–2 PROPN cana-1056 66 18 ( ( PUNCT cana-1056 66 19 32 32 NUM cana-1056 66 20 ) ) PUNCT cana-1056 66 21 where where SCONJ cana-1056 66 22 π‘§π‘˜ π‘§π‘˜ AUX cana-1056 66 23 = = SYM cana-1056 66 24 π‘¦π‘˜ π‘¦π‘˜ PROPN cana-1056 66 25 + + NOUN cana-1056 66 26 1 1 NUM cana-1056 66 27 3 3 NUM cana-1056 66 28 πœƒπ‘˜ πœƒπ‘˜ ADP cana-1056 66 29 β€–π‘ π‘˜β€–2 β€–π‘ π‘˜β€–2 PROPN cana-1056 66 30 π‘ π‘˜ π‘ π‘˜ PROPN cana-1056 67 1 [ [ X cana-1056 67 2 13 13 NUM cana-1056 67 3 ] ] PUNCT cana-1056 67 4 ( ( PUNCT cana-1056 67 5 33 33 NUM cana-1056 67 6 ) ) PUNCT cana-1056 67 7 and and CCONJ cana-1056 67 8 πœƒπ‘˜ πœƒπ‘˜ X cana-1056 67 9 = = SYM cana-1056 67 10 2(π‘“π‘˜ 2(π‘“π‘˜ NUM cana-1056 67 11 βˆ’ βˆ’ NOUN cana-1056 67 12 π‘“π‘˜+1 π‘“π‘˜+1 NOUN cana-1056 67 13 ) ) PUNCT cana-1056 67 14 + + CCONJ cana-1056 67 15 ( ( PUNCT cana-1056 67 16 π‘”π‘˜+1 π‘”π‘˜+1 NOUN cana-1056 67 17 + + CCONJ cana-1056 67 18 π‘”π‘˜)π‘‡π‘ π‘˜ π‘”π‘˜)π‘‡π‘ π‘˜ PROPN cana-1056 67 19 ( ( PUNCT cana-1056 67 20 34 34 NUM cana-1056 67 21 ) ) PUNCT cana-1056 67 22 and and CCONJ cana-1056 67 23 Ξ²k Ξ²k ADP cana-1056 67 24 n3 n3 NOUN cana-1056 67 25 = = PROPN cana-1056 67 26 gk gk PROPN cana-1056 67 27 t(zkβˆ’tsk t(zkβˆ’tsk PROPN cana-1056 67 28 ) ) PUNCT cana-1056 67 29 βˆ’gkβˆ’1 βˆ’gkβˆ’1 NUM cana-1056 67 30 t t X cana-1056 67 31 dkβˆ’1 dkβˆ’1 PROPN cana-1056 67 32 ( ( PUNCT cana-1056 67 33 35 35 NUM cana-1056 67 34 ) ) PUNCT cana-1056 67 35 where where SCONJ cana-1056 67 36 π‘§π‘˜ π‘§π‘˜ AUX cana-1056 67 37 = = SYM cana-1056 67 38 π‘¦π‘˜ π‘¦π‘˜ PROPN cana-1056 67 39 + + NOUN cana-1056 67 40 2 2 NUM cana-1056 67 41 3 3 NUM cana-1056 67 42 πœƒπ‘˜ πœƒπ‘˜ ADP cana-1056 67 43 β€–π‘ π‘˜β€–2 β€–π‘ π‘˜β€–2 PROPN cana-1056 67 44 π‘ π‘˜ π‘ π‘˜ PROPN cana-1056 67 45 [ [ X cana-1056 67 46 14 14 NUM cana-1056 67 47 ] ] X cana-1056 67 48 ( ( PUNCT cana-1056 67 49 36 36 NUM cana-1056 67 50 ) ) PUNCT cana-1056 67 51 πœƒπ‘˜ πœƒπ‘˜ NOUN cana-1056 68 1 = = SYM cana-1056 68 2 4(π‘“π‘˜βˆ’1 4(π‘“π‘˜βˆ’1 NUM cana-1056 68 3 βˆ’ βˆ’ NUM cana-1056 68 4 π‘“π‘˜ π‘“π‘˜ NOUN cana-1056 68 5 ) ) PUNCT cana-1056 69 1 + + CCONJ cana-1056 69 2 2(π‘”π‘˜ 2(π‘”π‘˜ NOUN cana-1056 69 3 + + CCONJ cana-1056 69 4 π‘”π‘˜+1)π‘‡π‘ π‘˜βˆ’1 π‘”π‘˜+1)π‘‡π‘ π‘˜βˆ’1 X cana-1056 70 1 [ [ X cana-1056 70 2 14][15 14][15 X cana-1056 70 3 ] ] X cana-1056 70 4 ( ( PUNCT cana-1056 70 5 37 37 NUM cana-1056 70 6 ) ) PUNCT cana-1056 70 7 2.1 2.1 NUM cana-1056 70 8 algorithm algorithm NOUN cana-1056 70 9 step1 step1 PROPN cana-1056 70 10 : : PUNCT cana-1056 70 11 take take VERB cana-1056 70 12 π‘₯0 π‘₯0 NOUN cana-1056 70 13 ∈ ∈ NOUN cana-1056 70 14 𝑅𝑛 𝑅𝑛 PROPN cana-1056 70 15 , , PUNCT cana-1056 70 16 and and CCONJ cana-1056 70 17 0 0 NUM cana-1056 70 18 < < X cana-1056 70 19 𝛿 𝛿 PROPN cana-1056 70 20 ≀ ≀ X cana-1056 70 21 𝜎 𝜎 X cana-1056 70 22 < < X cana-1056 70 23 1 1 NUM cana-1056 70 24 , , PUNCT cana-1056 70 25 calculate calculate NOUN cana-1056 70 26 𝑓(π‘₯0 𝑓(π‘₯0 NOUN cana-1056 70 27 ) ) PUNCT cana-1056 70 28 and and CCONJ cana-1056 70 29 𝑔0 𝑔0 NOUN cana-1056 70 30 = = SYM cana-1056 70 31 βˆ‡π‘“(π‘₯0 βˆ‡π‘“(π‘₯0 NUM cana-1056 70 32 ) ) PUNCT cana-1056 70 33 , , PUNCT cana-1056 70 34 set set VERB cana-1056 70 35 𝑑0 𝑑0 NOUN cana-1056 70 36 = = SYM cana-1056 70 37 βˆ’π‘”0 βˆ’π‘”0 NOUN cana-1056 70 38 for for ADP cana-1056 70 39 π‘˜ π‘˜ PRON cana-1056 70 40 = = SYM cana-1056 70 41 0 0 NUM cana-1056 70 42 communications communication NOUN cana-1056 70 43 on on ADP cana-1056 70 44 applied apply VERB cana-1056 70 45 nonlinear nonlinear ADJ cana-1056 70 46 analysis analysis NOUN cana-1056 70 47 issn issn NOUN cana-1056 70 48 : : PUNCT cana-1056 70 49 1074 1074 NUM cana-1056 70 50 - - PUNCT cana-1056 70 51 133x 133x NUM cana-1056 70 52 vol vol NOUN cana-1056 70 53 31 31 NUM cana-1056 70 54 no no NOUN cana-1056 70 55 . . PUNCT cana-1056 71 1 5s 5s NUM cana-1056 71 2 ( ( PUNCT cana-1056 71 3 2024 2024 NUM cana-1056 71 4 ) ) PUNCT cana-1056 71 5 376 376 NUM cana-1056 71 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 71 7 step2 step2 PROPN cana-1056 71 8 : : PUNCT cana-1056 71 9 compute compute AUX cana-1056 71 10 π›Όπ‘˜ π›Όπ‘˜ NOUN cana-1056 71 11 satisfying satisfy VERB cana-1056 71 12 strong strong ADJ cana-1056 71 13 " " PUNCT cana-1056 71 14 wolfe wolfe PROPN cana-1056 71 15 condition condition NOUN cana-1056 71 16 " " PUNCT cana-1056 71 17 ) ) PUNCT cana-1056 71 18 3.10 3.10 NUM cana-1056 71 19 ) ) PUNCT cana-1056 71 20 ( ( PUNCT cana-1056 71 21 3.11 3.11 NUM cana-1056 71 22 ) ) PUNCT cana-1056 71 23 and and CCONJ cana-1056 71 24 then then ADV cana-1056 71 25 compute compute VERB cana-1056 71 26 π‘₯π‘˜+1 π‘₯π‘˜+1 NOUN cana-1056 71 27 = = SYM cana-1056 71 28 π‘₯π‘˜ π‘₯π‘˜ X cana-1056 71 29 + + CCONJ cana-1056 71 30 π›Όπ‘˜π‘‘π‘˜ π›Όπ‘˜π‘‘π‘˜ PROPN cana-1056 71 31 step3 step3 PROPN cana-1056 71 32 : : PUNCT cana-1056 71 33 if(β€–π‘”π‘˜β€–βˆž if(β€–π‘”π‘˜β€–βˆž PROPN cana-1056 71 34 ≀ ≀ NUM cana-1056 71 35 10βˆ’10 10βˆ’10 NUM cana-1056 71 36 or or CCONJ cana-1056 71 37 ( ( PUNCT cana-1056 71 38 |π›Όπ‘˜π‘”π‘˜π‘‘π‘˜| |π›Όπ‘˜π‘”π‘˜π‘‘π‘˜| ADV cana-1056 71 39 ≀ ≀ NUM cana-1056 71 40 10βˆ’10|π‘“π‘˜| 10βˆ’10|π‘“π‘˜| NUM cana-1056 71 41 ) ) PUNCT cana-1056 71 42 is be AUX cana-1056 71 43 satisfy satisfy NOUN cana-1056 71 44 then then ADV cana-1056 71 45 stop stop VERB cana-1056 71 46 . . PUNCT cana-1056 72 1 step4 step4 PROPN cana-1056 72 2 : : PUNCT cana-1056 72 3 compute compute VERB cana-1056 72 4 the the DET cana-1056 72 5 new new ADJ cana-1056 72 6 search search NOUN cana-1056 72 7 direction direction NOUN cana-1056 72 8 : : PUNCT cana-1056 72 9 π‘‘π‘˜ π‘‘π‘˜ ADV cana-1056 72 10 = = PUNCT cana-1056 72 11 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ PROPN cana-1056 73 1 + + CCONJ cana-1056 73 2 π›½π‘˜π‘‘π‘˜βˆ’1 π›½π‘˜π‘‘π‘˜βˆ’1 PROPN cana-1056 73 3 if if SCONJ cana-1056 73 4 the the DET cana-1056 73 5 restart restart NOUN cana-1056 73 6 criterion criterion NOUN cana-1056 73 7 of of ADP cana-1056 73 8 powell powell PROPN cana-1056 73 9 , , PUNCT cana-1056 73 10 such such ADJ cana-1056 73 11 that that SCONJ cana-1056 73 12 |gk |gk PROPN cana-1056 73 13 tπ‘”π‘˜βˆ’1| tπ‘”π‘˜βˆ’1| X cana-1056 73 14 β‰₯ β‰₯ NOUN cana-1056 73 15 0.2β€–π‘”π‘˜β€–2 0.2β€–π‘”π‘˜β€–2 ADJ cana-1056 73 16 is be AUX cana-1056 73 17 satisfied satisfied ADJ cana-1056 73 18 , , PUNCT cana-1056 73 19 then then ADV cana-1056 73 20 set set VERB cana-1056 73 21 π‘‘π‘˜ π‘‘π‘˜ ADP cana-1056 73 22 = = SYM cana-1056 73 23 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ PROPN cana-1056 73 24 ; ; PUNCT cana-1056 73 25 otherwise otherwise ADV cana-1056 73 26 , , PUNCT cana-1056 73 27 define define VERB cana-1056 73 28 step5 step5 NOUN cana-1056 73 29 : : PUNCT cana-1056 73 30 compute compute VERB cana-1056 73 31 the the DET cana-1056 73 32 new new ADJ cana-1056 73 33 parameters parameter NOUN cana-1056 73 34 Ξ²k Ξ²k ADP cana-1056 73 35 n1 n1 NOUN cana-1056 73 36 , , PUNCT cana-1056 73 37 Ξ²k Ξ²k NOUN cana-1056 73 38 n2 n2 ADJ cana-1056 73 39 , , PUNCT cana-1056 73 40 Ξ²k Ξ²k VERB cana-1056 73 41 n3from(30,31,34)respectively n3from(30,31,34)respectively ADV cana-1056 73 42 step6 step6 NOUN cana-1056 73 43 : : PUNCT cana-1056 73 44 set set VERB cana-1056 73 45 𝐾 𝐾 PROPN cana-1056 73 46 = = SYM cana-1056 73 47 𝐾 𝐾 PROPN cana-1056 73 48 + + CCONJ cana-1056 73 49 1 1 NUM cana-1056 73 50 and and CCONJ cana-1056 73 51 go go VERB cana-1056 73 52 to to ADP cana-1056 73 53 step2 step2 PROPN cana-1056 73 54 . . PROPN cana-1056 74 1 3 3 X cana-1056 74 2 . . X cana-1056 74 3 convergence convergence NOUN cana-1056 74 4 analysis analysis NOUN cana-1056 74 5 3.1 3.1 NUM cana-1056 74 6 introductory introductory NOUN cana-1056 74 7 in in ADP cana-1056 74 8 this this DET cana-1056 74 9 section section NOUN cana-1056 74 10 we we PRON cana-1056 74 11 are be AUX cana-1056 74 12 position position NOUN cana-1056 74 13 verify verify VERB cana-1056 74 14 global global ADJ cana-1056 74 15 convergence convergence NOUN cana-1056 74 16 of of ADP cana-1056 74 17 the the DET cana-1056 74 18 new new ADJ cana-1056 74 19 methods method NOUN cana-1056 74 20 . . PUNCT cana-1056 75 1 3.1 3.1 NUM cana-1056 75 2 hypothesis hypothesis NOUN cana-1056 75 3 1 1 NUM cana-1056 75 4 : : PUNCT cana-1056 75 5 see see VERB cana-1056 75 6 [ [ X cana-1056 75 7 10 10 NUM cana-1056 75 8 ] ] PUNCT cana-1056 75 9 . . PUNCT cana-1056 76 1 dia dia PROPN cana-1056 76 2 et et PROPN cana-1056 76 3 al al PROPN cana-1056 76 4 . . PROPN cana-1056 76 5 demonstrated demonstrate VERB cana-1056 76 6 that that SCONJ cana-1056 76 7 any any DET cana-1056 76 8 cg cg NOUN cana-1056 76 9 algorithm algorithm NOUN cana-1056 76 10 utilizing utilize VERB cana-1056 76 11 the the DET cana-1056 76 12 powerful powerful ADJ cana-1056 76 13 wolf wolf PROPN cana-1056 76 14 line line NOUN cana-1056 76 15 search search NOUN cana-1056 76 16 yields yield VERB cana-1056 76 17 the the DET cana-1056 76 18 subsequent subsequent ADJ cana-1056 76 19 beneficial beneficial ADJ cana-1056 76 20 outcome outcome NOUN cana-1056 77 1 [ [ X cana-1056 77 2 16],[17 16],[17 PROPN cana-1056 77 3 ] ] SYM cana-1056 77 4 . . PUNCT cana-1056 78 1 3.2 3.2 NUM cana-1056 78 2 lemma lemma PROPN cana-1056 78 3 from from ADP cana-1056 78 4 he he PRON cana-1056 78 5 hypothesis hypothesis NOUN cana-1056 78 6 1 1 NUM cana-1056 78 7 holds hold VERB cana-1056 78 8 .we .we PUNCT cana-1056 78 9 have have VERB cana-1056 78 10 for for ADP cana-1056 78 11 any any DET cana-1056 78 12 cg cg NOUN cana-1056 78 13 method method NOUN cana-1056 78 14 in in ADP cana-1056 78 15 the the DET cana-1056 78 16 form form NOUN cana-1056 78 17 ( ( PUNCT cana-1056 78 18 2)-(3 2)-(3 NOUN cana-1056 78 19 ) ) PUNCT cana-1056 78 20 , , PUNCT cana-1056 78 21 where where SCONJ cana-1056 78 22 π‘‘π‘˜satisfies π‘‘π‘˜satisfie VERB cana-1056 78 23 the the DET cana-1056 78 24 d.c d.c PROPN cana-1056 78 25 . . PUNCT cana-1056 79 1 in in ADP cana-1056 79 2 ( ( PUNCT cana-1056 79 3 26 26 NUM cana-1056 79 4 ) ) PUNCT cana-1056 79 5 , , PUNCT cana-1056 79 6 where where SCONJ cana-1056 79 7 π›Όπ‘˜ π›Όπ‘˜ PRON cana-1056 79 8 is be AUX cana-1056 79 9 gets get VERB cana-1056 79 10 by by ADP cana-1056 79 11 the the DET cana-1056 79 12 strong strong ADJ cana-1056 79 13 wolf wolf PROPN cana-1056 79 14 line line NOUN cana-1056 79 15 search search NOUN cana-1056 79 16 ( ( PUNCT cana-1056 79 17 28)-(29 28)-(29 NOUN cana-1056 79 18 ) ) PUNCT cana-1056 79 19 . . PUNCT cana-1056 80 1 let let VERB cana-1056 80 2 πœ‘ πœ‘ PRON cana-1056 80 3 ∈ ∈ VERB cana-1056 81 1 [ [ X cana-1056 81 2 0,4 0,4 NOUN cana-1056 81 3 ] ] PUNCT cana-1056 81 4 be be VERB cana-1056 81 5 given[18 given[18 VERB cana-1056 81 6 ] ] PUNCT cana-1056 81 7 . . PUNCT cana-1056 82 1 if if SCONJ cana-1056 82 2 βˆ‘ βˆ‘ ADP cana-1056 82 3 β€–π‘”π‘˜β€–πœ‘ β€–π‘”π‘˜β€–πœ‘ PROPN cana-1056 82 4 β€–π‘”π‘˜β€–2 β€–π‘”π‘˜β€–2 PROPN cana-1056 82 5 = = SYM cana-1056 82 6 ∞ ∞ NUM cana-1056 82 7 π‘˜β‰₯1 π‘˜β‰₯1 PROPN cana-1056 82 8 then then ADV cana-1056 82 9 the the DET cana-1056 82 10 following follow VERB cana-1056 82 11 holds hold VERB cana-1056 82 12 lim lim PROPN cana-1056 82 13 π‘˜β†’βˆž π‘˜β†’βˆž NUM cana-1056 82 14 β€–π‘”π‘˜β€– β€–π‘”π‘˜β€– PROPN cana-1056 82 15 = = PUNCT cana-1056 82 16 0 0 NUM cana-1056 82 17 by by ADP cana-1056 82 18 then then ADV cana-1056 82 19 . . PUNCT cana-1056 82 20 . . PUNCT cana-1056 83 1 . . PUNCT cana-1056 84 1 if if SCONJ cana-1056 84 2 πœƒ πœƒ NUM cana-1056 84 3 = = SYM cana-1056 84 4 0 0 NUM cana-1056 84 5 β‡’ β‡’ PROPN cana-1056 84 6 limπ‘˜β†’βˆž limπ‘˜β†’βˆž PROPN cana-1056 84 7 β€Š β€Š SPACE cana-1056 84 8 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ PROPN cana-1056 84 9 = = SYM cana-1056 84 10 0 0 NUM cana-1056 84 11 3.3 3.3 NUM cana-1056 84 12 theorem theorem NOUN cana-1056 84 13 assuming assume VERB cana-1056 84 14 assumption assumption NOUN cana-1056 84 15 1 1 NUM cana-1056 84 16 is be AUX cana-1056 84 17 valid valid ADJ cana-1056 84 18 and and CCONJ cana-1056 84 19 f f PROPN cana-1056 84 20 is be AUX cana-1056 84 21 a a DET cana-1056 84 22 uniformly uniformly ADV cana-1056 84 23 convex convex NOUN cana-1056 84 24 function function NOUN cana-1056 84 25 , , PUNCT cana-1056 84 26 let let VERB cana-1056 84 27 's us PRON cana-1056 84 28 take take VERB cana-1056 84 29 a a DET cana-1056 84 30 look look NOUN cana-1056 84 31 at at ADP cana-1056 84 32 the the DET cana-1056 84 33 conjugate conjugate ADJ cana-1056 84 34 gradient gradient NOUN cana-1056 84 35 method method NOUN cana-1056 84 36 using use VERB cana-1056 84 37 equation equation NOUN cana-1056 84 38 ( ( PUNCT cana-1056 84 39 15 15 NUM cana-1056 84 40 ) ) PUNCT cana-1056 84 41 . . PUNCT cana-1056 85 1 in in ADP cana-1056 85 2 this this DET cana-1056 85 3 method method NOUN cana-1056 85 4 , , PUNCT cana-1056 85 5 the the DET cana-1056 85 6 values value NOUN cana-1056 85 7 of of ADP cana-1056 85 8 dk dk PROPN cana-1056 85 9 and and CCONJ cana-1056 85 10 π‘’π‘˜ π‘’π‘˜ PROPN cana-1056 85 11 must must AUX cana-1056 85 12 satisfy satisfy VERB cana-1056 85 13 the the DET cana-1056 85 14 descent descent NOUN cana-1056 85 15 condition condition NOUN cana-1056 85 16 ( ( PUNCT cana-1056 85 17 26 26 NUM cana-1056 85 18 ) ) PUNCT cana-1056 85 19 and and CCONJ cana-1056 85 20 condition condition NOUN cana-1056 85 21 ( ( PUNCT cana-1056 85 22 5.9 5.9 NUM cana-1056 85 23 ) ) PUNCT cana-1056 85 24 respectively respectively ADV cana-1056 85 25 , , PUNCT cana-1056 85 26 while while SCONJ cana-1056 85 27 Ξ±k Ξ±k ADV cana-1056 85 28 is be AUX cana-1056 85 29 determined determine VERB cana-1056 85 30 through through ADP cana-1056 85 31 the the DET cana-1056 85 32 strong strong ADJ cana-1056 85 33 wolfe wolfe PROPN cana-1056 85 34 line line NOUN cana-1056 85 35 search search NOUN cana-1056 85 36 algorithm algorithm NOUN cana-1056 85 37 . . PUNCT cana-1056 86 1 if if SCONJ cana-1056 86 2 𝐿 𝐿 PROPN cana-1056 86 3 = = PUNCT cana-1056 86 4 πœ‡ πœ‡ ADP cana-1056 86 5 then then ADV cana-1056 86 6 our our PRON cana-1056 86 7 method method NOUN cana-1056 86 8 with with ADP cana-1056 86 9 𝜌 𝜌 ADP cana-1056 86 10 β‰₯ β‰₯ X cana-1056 86 11 0 0 NUM cana-1056 86 12 satisfies satisfie NOUN cana-1056 86 13 lim lim PROPN cana-1056 86 14 π‘˜β†’βˆž π‘˜β†’βˆž PUNCT cana-1056 86 15 β€–π‘”π‘˜β€– β€–π‘”π‘˜β€– PROPN cana-1056 86 16 = = PUNCT cana-1056 86 17 0 0 X cana-1056 86 18 . . PUNCT cana-1056 87 1 if if SCONJ cana-1056 87 2 l l PROPN cana-1056 87 3 > > X cana-1056 87 4 πœ‡ πœ‡ ADP cana-1056 87 5 , , PUNCT cana-1056 87 6 then then ADV cana-1056 87 7 our our PRON cana-1056 87 8 method method NOUN cana-1056 87 9 0 0 NUM cana-1056 87 10 ≀ ≀ NUM cana-1056 87 11 𝜌 𝜌 ADP cana-1056 87 12 < < X cana-1056 87 13 𝐿 𝐿 PROPN cana-1056 87 14 3(πΏβˆ’πœ‡ 3(πΏβˆ’πœ‡ NOUN cana-1056 87 15 ) ) PUNCT cana-1056 87 16 satisfies satisfie NOUN cana-1056 87 17 lim lim PROPN cana-1056 87 18 π‘˜β†’βˆž π‘˜β†’βˆž PUNCT cana-1056 88 1 β€–π‘”π‘˜β€– β€–π‘”π‘˜β€– PROPN cana-1056 88 2 = = SYM cana-1056 88 3 0 0 X cana-1056 88 4 . . PUNCT cana-1056 89 1 communications communication NOUN cana-1056 89 2 on on ADP cana-1056 89 3 applied apply VERB cana-1056 89 4 nonlinear nonlinear ADJ cana-1056 89 5 analysis analysis NOUN cana-1056 89 6 issn issn NOUN cana-1056 89 7 : : PUNCT cana-1056 89 8 1074 1074 NUM cana-1056 89 9 - - PUNCT cana-1056 89 10 133x 133x NUM cana-1056 89 11 vol vol NOUN cana-1056 89 12 31 31 NUM cana-1056 89 13 no no NOUN cana-1056 89 14 . . PUNCT cana-1056 90 1 5s 5s NUM cana-1056 90 2 ( ( PUNCT cana-1056 90 3 2024 2024 NUM cana-1056 90 4 ) ) PUNCT cana-1056 90 5 377 377 NUM cana-1056 90 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 90 7 proof proof NOUN cana-1056 90 8 : : PUNCT cana-1056 90 9 from from ADP cana-1056 90 10 paper paper NOUN cana-1056 90 11 [ [ X cana-1056 90 12 10]we 10]we X cana-1056 90 13 have have VERB cana-1056 90 14 that that PRON cana-1056 90 15 from from ADP cana-1056 90 16 { { PUNCT cana-1056 90 17 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 90 18 = = PROPN cana-1056 90 19 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 90 20 + + PROPN cana-1056 90 21 ρ ρ PROPN cana-1056 90 22 ( ( PUNCT cana-1056 90 23 πœƒπ‘˜βˆ’1 πœƒπ‘˜βˆ’1 PROPN cana-1056 90 24 π‘ π‘˜ π‘ π‘˜ NOUN cana-1056 90 25 π‘‡π‘’π‘˜βˆ’1 π‘‡π‘’π‘˜βˆ’1 PROPN cana-1056 90 26 ) ) PUNCT cana-1056 90 27 πœƒπ‘˜βˆ’1 πœƒπ‘˜βˆ’1 VERB cana-1056 90 28 = = PUNCT cana-1056 91 1 6(π‘“π‘˜βˆ’1 6(π‘“π‘˜βˆ’1 NUM cana-1056 91 2 βˆ’ βˆ’ NOUN cana-1056 91 3 π‘“π‘˜ π‘“π‘˜ NOUN cana-1056 91 4 ) ) PUNCT cana-1056 91 5 + + CCONJ cana-1056 91 6 3(gkβˆ’1 3(gkβˆ’1 NUM cana-1056 91 7 + + NUM cana-1056 91 8 gk)π‘‡π‘ π‘˜βˆ’1 gk)π‘‡π‘ π‘˜βˆ’1 PROPN cana-1056 91 9 and and CCONJ cana-1056 91 10 π‘“π‘˜βˆ’1 π‘“π‘˜βˆ’1 PROPN cana-1056 91 11 βˆ’ βˆ’ PROPN cana-1056 91 12 π‘“π‘˜ π‘“π‘˜ PRON cana-1056 91 13 β‰₯ β‰₯ NOUN cana-1056 91 14 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 91 15 π‘‡π‘ π‘˜βˆ’1 π‘‡π‘ π‘˜βˆ’1 NOUN cana-1056 91 16 + + CCONJ cana-1056 91 17 πœ‡ πœ‡ DET cana-1056 91 18 2 2 NUM cana-1056 91 19 β€–π‘ π‘˜βˆ’1β€–2 β€–π‘ π‘˜βˆ’1β€–2 NOUN cana-1056 91 20 and and CCONJ cana-1056 91 21 πœ‡β€–π‘ π‘˜βˆ’1β€–2 πœ‡β€–π‘ π‘˜βˆ’1β€–2 PROPN cana-1056 91 22 ≀ ≀ PROPN cana-1056 91 23 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 91 24 𝑇 𝑇 PROPN cana-1056 91 25 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 91 26 ≀ ≀ NUM cana-1056 91 27 πΏβ€–π‘ π‘˜βˆ’1β€–2 πΏβ€–π‘ π‘˜βˆ’1β€–2 NOUN cana-1056 91 28 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 NOUN cana-1056 91 29 𝑇 𝑇 PROPN cana-1056 91 30 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 91 31 = = PROPN cana-1056 91 32 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 91 33 𝑇 𝑇 PROPN cana-1056 91 34 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 91 35 + + PROPN cana-1056 91 36 πœŒπœƒπ‘˜βˆ’1 πœŒπœƒπ‘˜βˆ’1 PROPN cana-1056 91 37 = = SYM cana-1056 91 38 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 91 39 𝑇 𝑇 PROPN cana-1056 91 40 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 91 41 + + PROPN cana-1056 92 1 6𝜌(π‘“π‘˜βˆ’1 6𝜌(π‘“π‘˜βˆ’1 PROPN cana-1056 92 2 βˆ’ βˆ’ NUM cana-1056 92 3 π‘“π‘˜ π‘“π‘˜ NOUN cana-1056 92 4 ) ) PUNCT cana-1056 92 5 + + CCONJ cana-1056 92 6 3𝜌(π‘”π‘˜βˆ’1 3𝜌(π‘”π‘˜βˆ’1 NUM cana-1056 92 7 + + CCONJ cana-1056 92 8 π‘”π‘˜)π‘‡π‘ π‘˜βˆ’1 π‘”π‘˜)π‘‡π‘ π‘˜βˆ’1 PROPN cana-1056 92 9 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 92 10 = = PUNCT cana-1056 92 11 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 92 12 + + CCONJ cana-1056 92 13 𝜌 𝜌 X cana-1056 92 14 ( ( PUNCT cana-1056 92 15 πœƒπ‘˜βˆ’1 πœƒπ‘˜βˆ’1 PROPN cana-1056 92 16 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 92 17 πœ‹ πœ‹ PROPN cana-1056 92 18 π‘’π‘˜βˆ’1 π‘’π‘˜βˆ’1 PROPN cana-1056 92 19 π‘’π‘˜βˆ’1 π‘’π‘˜βˆ’1 PROPN cana-1056 92 20 ) ) PUNCT cana-1056 92 21 . . PUNCT cana-1056 93 1 πœƒπ‘˜βˆ’1 πœƒπ‘˜βˆ’1 NOUN cana-1056 93 2 = = PUNCT cana-1056 94 1 6(π‘“π‘˜βˆ’1 6(π‘“π‘˜βˆ’1 NUM cana-1056 94 2 βˆ’ βˆ’ NOUN cana-1056 94 3 π‘“π‘˜ π‘“π‘˜ NOUN cana-1056 94 4 ) ) PUNCT cana-1056 94 5 + + CCONJ cana-1056 94 6 3(π‘”π‘˜βˆ’1 3(π‘”π‘˜βˆ’1 NUM cana-1056 94 7 + + NUM cana-1056 94 8 π‘”π‘˜)βŠ€π‘ π‘˜βˆ’1 π‘”π‘˜)βŠ€π‘ π‘˜βˆ’1 PROPN cana-1056 94 9 π»π‘˜π‘§π‘˜βˆ’1 π»π‘˜π‘§π‘˜βˆ’1 VERB cana-1056 94 10 = = PUNCT cana-1056 94 11 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 94 12 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 94 13 ⊀ ⊀ PROPN cana-1056 94 14 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 94 15 = = PROPN cana-1056 94 16 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 94 17 ⊀ ⊀ PROPN cana-1056 94 18 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 94 19 + + PROPN cana-1056 94 20 πœŒπœƒπ‘˜βˆ’1 πœŒπœƒπ‘˜βˆ’1 PROPN cana-1056 94 21 = = SYM cana-1056 94 22 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 94 23 𝑇 𝑇 PROPN cana-1056 94 24 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 94 25 + + PROPN cana-1056 95 1 6𝜌(π‘“π‘˜βˆ’1 6𝜌(π‘“π‘˜βˆ’1 PROPN cana-1056 95 2 βˆ’ βˆ’ NUM cana-1056 95 3 π‘“π‘˜ π‘“π‘˜ NOUN cana-1056 95 4 ) ) PUNCT cana-1056 95 5 + + CCONJ cana-1056 95 6 3𝜌(π‘”π‘˜βˆ’1 3𝜌(π‘”π‘˜βˆ’1 NUM cana-1056 95 7 + + CCONJ cana-1056 95 8 π‘”π‘˜)π‘‡π‘ π‘˜βˆ’1 π‘”π‘˜)π‘‡π‘ π‘˜βˆ’1 PROPN cana-1056 95 9 β‰₯π‘ π‘˜βˆ’1 β‰₯π‘ π‘˜βˆ’1 PROPN cana-1056 95 10 ⊀ ⊀ PROPN cana-1056 95 11 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 95 12 + + PROPN cana-1056 95 13 6𝜌 6𝜌 NUM cana-1056 95 14 ( ( PUNCT cana-1056 95 15 βˆ’π‘”π‘˜ βˆ’π‘”π‘˜ X cana-1056 95 16 βŠ€π‘ π‘˜βˆ’1 βŠ€π‘ π‘˜βˆ’1 X cana-1056 95 17 + + CCONJ cana-1056 95 18 πœ‡ πœ‡ DET cana-1056 95 19 2 2 NUM cana-1056 95 20 βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 NOUN cana-1056 95 21 ) ) PUNCT cana-1056 96 1 + + NUM cana-1056 96 2 𝜌3(π‘”π‘˜βˆ’1 𝜌3(π‘”π‘˜βˆ’1 PUNCT cana-1056 96 3 + + CCONJ cana-1056 96 4 π‘”π‘˜)π‘‡π‘ π‘˜βˆ’1 π‘”π‘˜)π‘‡π‘ π‘˜βˆ’1 X cana-1056 96 5 = = PUNCT cana-1056 96 6 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 96 7 𝑇 𝑇 PROPN cana-1056 96 8 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 96 9 βˆ’ βˆ’ PROPN cana-1056 96 10 3πœŒπ‘”π‘˜ 3πœŒπ‘”π‘˜ NUM cana-1056 96 11 π‘‡π‘ π‘˜βˆ’1 π‘‡π‘ π‘˜βˆ’1 NOUN cana-1056 96 12 + + NUM cana-1056 96 13 3πœŒπ‘”π‘˜βˆ’1 3πœŒπ‘”π‘˜βˆ’1 NUM cana-1056 96 14 𝑇 𝑇 PROPN cana-1056 96 15 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 96 16 + + PROPN cana-1056 96 17 3πœŒπœ‡βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 3πœŒπœ‡βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 NUM cana-1056 96 18 = = NOUN cana-1056 96 19 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 96 20 𝑇 𝑇 PROPN cana-1056 96 21 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 96 22 βˆ’ βˆ’ PROPN cana-1056 96 23 3πœŒπ‘ π‘˜βˆ’1 3πœŒπ‘ π‘˜βˆ’1 NUM cana-1056 96 24 𝑇 𝑇 PROPN cana-1056 96 25 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 96 26 + + PROPN cana-1056 97 1 3πœŒπœ‡βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 3πœŒπœ‡βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 NUM cana-1056 97 2 = = SYM cana-1056 97 3 ( ( PUNCT cana-1056 97 4 1 1 NUM cana-1056 97 5 βˆ’ βˆ’ PROPN cana-1056 97 6 3𝜌)π‘ π‘˜βˆ’1 3𝜌)π‘ π‘˜βˆ’1 PROPN cana-1056 97 7 𝑇 𝑇 PROPN cana-1056 97 8 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 97 9 + + PROPN cana-1056 98 1 3πœŒπœ‡βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 3πœŒπœ‡βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 NUM cana-1056 98 2 β‰₯ β‰₯ NOUN cana-1056 98 3 ( ( PUNCT cana-1056 98 4 1 1 NUM cana-1056 98 5 βˆ’ βˆ’ PROPN cana-1056 98 6 3𝜌)π‘ π‘˜βˆ’1 3𝜌)π‘ π‘˜βˆ’1 PROPN cana-1056 98 7 𝑇 𝑇 PROPN cana-1056 98 8 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 98 9 + + PROPN cana-1056 98 10 3πœŒπœ‡ 3πœŒπœ‡ PROPN cana-1056 98 11 𝐿 𝐿 PROPN cana-1056 98 12 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 98 13 𝑇 𝑇 PROPN cana-1056 98 14 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 98 15 = = PUNCT cana-1056 98 16 πΏβˆ’3𝜌(πΏβˆ’πœ‡ πΏβˆ’3𝜌(πΏβˆ’πœ‡ NUM cana-1056 98 17 ) ) PUNCT cana-1056 98 18 𝐿 𝐿 PROPN cana-1056 98 19 π‘†π‘˜βˆ’1 π‘†π‘˜βˆ’1 PROPN cana-1056 98 20 𝑇 𝑇 PROPN cana-1056 98 21 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 98 22 ( ( PUNCT cana-1056 98 23 38 38 NUM cana-1056 98 24 ) ) PUNCT cana-1056 98 25 we we PRON cana-1056 98 26 have have VERB cana-1056 98 27 0 0 NUM cana-1056 98 28 ≀ ≀ NUM cana-1056 98 29 𝜌 𝜌 ADP cana-1056 98 30 < < X cana-1056 98 31 𝐿 𝐿 PROPN cana-1056 98 32 3(πΏβˆ’πœ‡ 3(πΏβˆ’πœ‡ NOUN cana-1056 98 33 ) ) PUNCT cana-1056 98 34 , , PUNCT cana-1056 98 35 and and CCONJ cana-1056 98 36 we we PRON cana-1056 98 37 have have VERB cana-1056 98 38 : : PUNCT cana-1056 98 39 π‘ π‘˜βˆ’1 π‘ π‘˜βˆ’1 PROPN cana-1056 98 40 𝑇 𝑇 PROPN cana-1056 98 41 π‘§π‘˜βˆ’1 π‘§π‘˜βˆ’1 PROPN cana-1056 98 42 β‰₯ β‰₯ PROPN cana-1056 98 43 { { PUNCT cana-1056 98 44 𝐿 𝐿 PROPN cana-1056 98 45 βˆ’ βˆ’ PROPN cana-1056 98 46 3𝜌(𝐿 3𝜌(𝐿 NUM cana-1056 98 47 βˆ’ βˆ’ NOUN cana-1056 98 48 πœ‡ πœ‡ ADP cana-1056 98 49 𝐿 𝐿 PROPN cana-1056 98 50 } } PUNCT cana-1056 98 51 πœ‡β€–π‘ π‘˜βˆ’1β€–2 πœ‡β€–π‘ π‘˜βˆ’1β€–2 PROPN cana-1056 98 52 βˆ₯βˆ₯π‘‘π‘˜βˆ₯βˆ₯ βˆ₯βˆ₯π‘‘π‘˜βˆ₯βˆ₯ NOUN cana-1056 98 53 = = PUNCT cana-1056 98 54 βˆ₯βˆ₯βˆ’π‘”π‘˜ βˆ₯βˆ₯βˆ’π‘”π‘˜ PROPN cana-1056 98 55 + + PUNCT cana-1056 98 56 π›½π‘˜π‘‘π‘˜βˆ’1βˆ₯βˆ₯ π›½π‘˜π‘‘π‘˜βˆ’1βˆ₯βˆ₯ NOUN cana-1056 98 57 = = PUNCT cana-1056 98 58 βˆ₯βˆ₯ βˆ₯βˆ₯ X cana-1056 98 59 βˆ₯βˆ₯βˆ’π‘”π‘˜ βˆ₯βˆ₯βˆ’π‘”π‘˜ PUNCT cana-1056 99 1 + + CCONJ cana-1056 99 2 π‘”π‘˜ π‘”π‘˜ ADP cana-1056 99 3 ⊀(π‘¦π‘˜ ⊀(π‘¦π‘˜ PUNCT cana-1056 99 4 βˆ’ βˆ’ PUNCT cana-1056 99 5 π‘‘π‘ π‘˜βˆ’1 π‘‘π‘ π‘˜βˆ’1 NOUN cana-1056 99 6 ) ) PUNCT cana-1056 99 7 π‘‘π‘˜βˆ’1 π‘‘π‘˜βˆ’1 PROPN cana-1056 99 8 ⊀ ⊀ PROPN cana-1056 99 9 π‘¦π‘˜βˆ’1 π‘¦π‘˜βˆ’1 PROPN cana-1056 99 10 π‘‘π‘˜βˆ’1 π‘‘π‘˜βˆ’1 PROPN cana-1056 99 11 βˆ₯βˆ₯ βˆ₯βˆ₯ X cana-1056 99 12 βˆ₯βˆ₯ βˆ₯βˆ₯ X cana-1056 99 13 ≀ ≀ PROPN cana-1056 99 14 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ PROPN cana-1056 99 15 + + NUM cana-1056 99 16 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯(βˆ₯βˆ₯π‘¦π‘˜βˆ’1βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯(βˆ₯βˆ₯π‘¦π‘˜βˆ’1βˆ₯βˆ₯ NOUN cana-1056 99 17 + + NUM cana-1056 99 18 𝑑βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ 𝑑βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ NOUN cana-1056 99 19 |π‘‘π‘˜βˆ’1 |π‘‘π‘˜βˆ’1 NUM cana-1056 99 20 𝜏 𝜏 DET cana-1056 99 21 π‘¦π‘˜βˆ’1| π‘¦π‘˜βˆ’1| NOUN cana-1056 99 22 βˆ₯βˆ₯π‘‘π‘˜βˆ’1βˆ₯βˆ₯ βˆ₯βˆ₯π‘‘π‘˜βˆ’1βˆ₯βˆ₯ VERB cana-1056 99 23 ≀ ≀ PROPN cana-1056 99 24 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ PROPN cana-1056 99 25 + + NUM cana-1056 99 26 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯(𝐹βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯(𝐹βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ NOUN cana-1056 99 27 + + CCONJ cana-1056 99 28 𝑑βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ 𝑑βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ NOUN cana-1056 99 29 |π‘ π‘˜βˆ’1 |π‘ π‘˜βˆ’1 NUM cana-1056 99 30 𝑇 𝑇 PROPN cana-1056 99 31 π‘§π‘˜βˆ’1| π‘§π‘˜βˆ’1| ADV cana-1056 99 32 βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯ NOUN cana-1056 99 33 communications communication NOUN cana-1056 99 34 on on ADP cana-1056 99 35 applied apply VERB cana-1056 99 36 nonlinear nonlinear ADJ cana-1056 99 37 analysis analysis NOUN cana-1056 99 38 issn issn NOUN cana-1056 99 39 : : PUNCT cana-1056 99 40 1074 1074 NUM cana-1056 99 41 - - PUNCT cana-1056 99 42 133x 133x NUM cana-1056 99 43 vol vol NOUN cana-1056 99 44 31 31 NUM cana-1056 99 45 no no NOUN cana-1056 99 46 . . PUNCT cana-1056 100 1 5s 5s NUM cana-1056 100 2 ( ( PUNCT cana-1056 100 3 2024 2024 NUM cana-1056 100 4 ) ) PUNCT cana-1056 100 5 378 378 NUM cana-1056 100 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 100 7 ≀ ≀ PROPN cana-1056 100 8 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ PROPN cana-1056 100 9 + + CCONJ cana-1056 100 10 ( ( PUNCT cana-1056 100 11 𝐹 𝐹 PROPN cana-1056 100 12 + + CCONJ cana-1056 100 13 t)βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ t)βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ NUM cana-1056 100 14 βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 NOUN cana-1056 100 15 𝑓1βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 𝑓1βˆ₯βˆ₯π‘ π‘˜βˆ’1βˆ₯βˆ₯2 NOUN cana-1056 100 16 = = PUNCT cana-1056 100 17 ( ( PUNCT cana-1056 100 18 1 1 NUM cana-1056 100 19 + + NUM cana-1056 100 20 𝐹 𝐹 PROPN cana-1056 100 21 + + CCONJ cana-1056 100 22 𝑑 𝑑 PROPN cana-1056 100 23 𝑓1 𝑓1 ADJ cana-1056 100 24 ) ) PUNCT cana-1056 100 25 βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ βˆ₯βˆ₯π‘”π‘˜βˆ₯βˆ₯ PROPN cana-1056 100 26 ≀ ≀ NOUN cana-1056 100 27 ( ( PUNCT cana-1056 100 28 𝑓1 𝑓1 PROPN cana-1056 100 29 + + CCONJ cana-1056 100 30 𝐹 𝐹 PROPN cana-1056 100 31 + + CCONJ cana-1056 100 32 𝑑) 𝑑) PROPN cana-1056 100 33 οΏ½ οΏ½ NOUN cana-1056 100 34 Μ… Μ… NOUN cana-1056 100 35 οΏ½ οΏ½ PROPN cana-1056 100 36 𝑓1 𝑓1 PROPN cana-1056 100 37 βˆ‘ βˆ‘ PROPN cana-1056 100 38 1 1 NUM cana-1056 100 39 βˆ₯ βˆ₯ NUM cana-1056 100 40 𝑑1𝑑|2 𝑑1𝑑|2 PROPN cana-1056 100 41 β‰₯ β‰₯ X cana-1056 100 42 { { PUNCT cana-1056 100 43 𝑓1 𝑓1 PROPN cana-1056 100 44 ( ( PUNCT cana-1056 100 45 𝑓1 𝑓1 PROPN cana-1056 100 46 + + CCONJ cana-1056 100 47 𝐹 𝐹 PROPN cana-1056 100 48 + + CCONJ cana-1056 100 49 𝑑)𝛾 𝑑)𝛾 PUNCT cana-1056 100 50 } } PUNCT cana-1056 100 51 2 2 NUM cana-1056 100 52 βˆ‘ βˆ‘ NOUN cana-1056 100 53 β€Š β€Š SPACE cana-1056 100 54 π‘˜β‰₯1 π‘˜β‰₯1 PROPN cana-1056 100 55 β€Š β€Š SPACE cana-1056 100 56 1 1 PROPN cana-1056 100 57 = = SYM cana-1056 100 58 ∞ ∞ NUM cana-1056 100 59 by by ADP cana-1056 100 60 theorem theorem NOUN cana-1056 100 61 3 3 NUM cana-1056 100 62 . . PUNCT cana-1056 101 1 if if SCONJ cana-1056 101 2 𝜎 𝜎 PRON cana-1056 101 3 = = SYM cana-1056 101 4 0 0 PROPN cana-1056 101 5 β‡’ β‡’ PROPN cana-1056 101 6 lim lim PROPN cana-1056 101 7 π‘˜β†’βˆž π‘˜β†’βˆž PUNCT cana-1056 101 8 β€–π‘”π‘˜β€– β€–π‘”π‘˜β€– PROPN cana-1056 101 9 = = SYM cana-1056 101 10 0 0 NUM cana-1056 101 11 4 4 NUM cana-1056 101 12 . . PUNCT cana-1056 101 13 numerical numerical ADJ cana-1056 101 14 results result NOUN cana-1056 101 15 this this DET cana-1056 101 16 section section NOUN cana-1056 101 17 provides provide VERB cana-1056 101 18 the the DET cana-1056 101 19 numerical numerical ADJ cana-1056 101 20 results result NOUN cana-1056 101 21 that that PRON cana-1056 101 22 assessed assess VERB cana-1056 101 23 the the DET cana-1056 101 24 effectiveness effectiveness NOUN cana-1056 101 25 of of ADP cana-1056 101 26 the the DET cana-1056 101 27 conjugate conjugate ADJ cana-1056 101 28 gradient gradient NOUN cana-1056 101 29 algorithms algorithm NOUN cana-1056 101 30 employing employ VERB cana-1056 101 31 the the DET cana-1056 101 32 fletcher fletcher PROPN cana-1056 101 33 - - PUNCT cana-1056 101 34 reeves reeves PROPN cana-1056 101 35 ( ( PUNCT cana-1056 101 36 fr fr PROPN cana-1056 101 37 ) ) PUNCT cana-1056 101 38 , , PUNCT cana-1056 101 39 polak polak PROPN cana-1056 101 40 - - PUNCT cana-1056 101 41 ribiere ribiere NOUN cana-1056 101 42 ( ( PUNCT cana-1056 101 43 pr pr NOUN cana-1056 101 44 ) ) PUNCT cana-1056 101 45 , , PUNCT cana-1056 101 46 and and CCONJ cana-1056 101 47 liu liu PROPN cana-1056 101 48 - - PUNCT cana-1056 101 49 storey storey NOUN cana-1056 101 50 ( ( PUNCT cana-1056 101 51 ls ls PROPN cana-1056 101 52 ) ) PUNCT cana-1056 101 53 techniques technique NOUN cana-1056 101 54 . . PUNCT cana-1056 102 1 this this DET cana-1056 102 2 information information NOUN cana-1056 102 3 is be AUX cana-1056 102 4 also also ADV cana-1056 102 5 available available ADJ cana-1056 102 6 in in ADP cana-1056 102 7 reference reference NOUN cana-1056 102 8 [ [ X cana-1056 102 9 19 19 NUM cana-1056 102 10 ] ] PUNCT cana-1056 102 11 . . PUNCT cana-1056 103 1 the the DET cana-1056 103 2 program program NOUN cana-1056 103 3 's 's PART cana-1056 103 4 requirements requirement NOUN cana-1056 103 5 for for ADP cana-1056 103 6 stopping stop VERB cana-1056 103 7 β€–π‘”π‘˜+1β€– β€–π‘”π‘˜+1β€– PROPN cana-1056 103 8 ≀ ≀ NUM cana-1056 103 9 10βˆ’5 10βˆ’5 NUM cana-1056 103 10 and and CCONJ cana-1056 103 11 written write VERB cana-1056 103 12 in in ADP cana-1056 103 13 ( ( PUNCT cana-1056 103 14 fortran90 fortran90 PROPN cana-1056 103 15 ) ) PUNCT cana-1056 103 16 . . PUNCT cana-1056 104 1 table table NOUN cana-1056 104 2 1 1 NUM cana-1056 104 3 shows show VERB cana-1056 104 4 the the DET cana-1056 104 5 number number NOUN cana-1056 104 6 of of ADP cana-1056 104 7 the the DET cana-1056 104 8 function function NOUN cana-1056 104 9 ( ( PUNCT cana-1056 104 10 nof nof PROPN cana-1056 104 11 ) ) PUNCT cana-1056 104 12 and and CCONJ cana-1056 104 13 the the DET cana-1056 104 14 number number NOUN cana-1056 104 15 of of ADP cana-1056 104 16 the the DET cana-1056 104 17 iteration iteration NOUN cana-1056 104 18 ( ( PUNCT cana-1056 104 19 noi noi PROPN cana-1056 104 20 ) ) PUNCT cana-1056 104 21 and and CCONJ cana-1056 104 22 confirms confirm VERB cana-1056 104 23 that that SCONJ cana-1056 104 24 the the DET cana-1056 104 25 new new ADJ cana-1056 104 26 methods method NOUN cana-1056 104 27 are be AUX cana-1056 104 28 superior superior ADJ cana-1056 104 29 ( ( PUNCT cana-1056 104 30 ni ni PROPN cana-1056 104 31 ) ) PUNCT cana-1056 104 32 with with ADP cana-1056 104 33 dimension dimension NOUN cana-1056 104 34 n=1000 n=1000 PROPN cana-1056 104 35 , , PUNCT cana-1056 104 36 10000[19],[20 10000[19],[20 NOUN cana-1056 104 37 ] ] X cana-1056 104 38 table table NOUN cana-1056 104 39 ( ( PUNCT cana-1056 104 40 1 1 X cana-1056 104 41 ) ) PUNCT cana-1056 104 42 comparison comparison NOUN cana-1056 104 43 between between ADP cana-1056 104 44 the the DET cana-1056 104 45 new new ADJ cana-1056 104 46 𝛽𝑁1 𝛽𝑁1 PROPN cana-1056 104 47 , , PUNCT cana-1056 104 48 𝛽𝑁2 𝛽𝑁2 PROPN cana-1056 104 49 , , PUNCT cana-1056 104 50 𝛽𝑁3 𝛽𝑁3 VERB cana-1056 104 51 methods method NOUN cana-1056 104 52 against against ADP cana-1056 104 53 𝛽𝐻𝑆 𝛽𝐻𝑆 PROPN cana-1056 104 54 , , PUNCT cana-1056 104 55 𝛽𝑃𝑅 𝛽𝑃𝑅 PROPN cana-1056 104 56 , , PUNCT cana-1056 104 57 𝛽𝐿𝑆 𝛽𝐿𝑆 VERB cana-1056 104 58 methods method NOUN cana-1056 104 59 for for ADP cana-1056 104 60 the the DET cana-1056 104 61 total total NOUN cana-1056 104 62 of of ADP cana-1056 104 63 30 30 NUM cana-1056 104 64 - - PUNCT cana-1056 104 65 problems problem NOUN cana-1056 104 66 with with ADP cana-1056 104 67 n=1000 n=1000 PROPN cana-1056 104 68 , , PUNCT cana-1056 104 69 10000 10000 NUM cana-1056 104 70 𝛽𝑁1 𝛽𝑁1 NUM cana-1056 104 71 𝛽𝑁2 𝛽𝑁2 PROPN cana-1056 104 72 𝛽𝑁3 𝛽𝑁3 PROPN cana-1056 104 73 Ξ²hs Ξ²hs NOUN cana-1056 104 74 𝛽𝑃𝑅 𝛽𝑃𝑅 PROPN cana-1056 104 75 𝛽𝐿𝑆 𝛽𝐿𝑆 VERB cana-1056 104 76 n n PRON cana-1056 104 77 p.no p.no PROPN cana-1056 104 78 . . PROPN cana-1056 104 79 fns fns PROPN cana-1056 104 80 nof nof PROPN cana-1056 104 81 noi noi PROPN cana-1056 104 82 nof nof PROPN cana-1056 104 83 noi noi PROPN cana-1056 104 84 nof nof PROPN cana-1056 104 85 noi noi PROPN cana-1056 104 86 nof nof PROPN cana-1056 104 87 noi noi PROPN cana-1056 104 88 nof nof PROPN cana-1056 104 89 noi noi PROPN cana-1056 104 90 nof nof PROPN cana-1056 104 91 noi noi PROPN cana-1056 104 92 71 71 NUM cana-1056 104 93 23 23 NUM cana-1056 104 94 76 76 NUM cana-1056 104 95 26 26 NUM cana-1056 104 96 77 77 NUM cana-1056 104 97 27 27 NUM cana-1056 104 98 103 103 NUM cana-1056 104 99 52 52 NUM cana-1056 104 100 103 103 NUM cana-1056 104 101 53 53 NUM cana-1056 104 102 102 102 NUM cana-1056 104 103 52 52 NUM cana-1056 104 104 1000 1000 NUM cana-1056 104 105 1 1 NUM cana-1056 104 106 80 80 NUM cana-1056 104 107 29 29 NUM cana-1056 104 108 82 82 NUM cana-1056 104 109 32 32 NUM cana-1056 104 110 80 80 NUM cana-1056 104 111 29 29 NUM cana-1056 104 112 124 124 NUM cana-1056 104 113 49 49 NUM cana-1056 104 114 127 127 NUM cana-1056 104 115 52 52 NUM cana-1056 104 116 132 132 NUM cana-1056 104 117 51 51 NUM cana-1056 104 118 10000 10000 NUM cana-1056 104 119 70 70 NUM cana-1056 104 120 13 13 NUM cana-1056 104 121 80 80 NUM cana-1056 104 122 19 19 NUM cana-1056 104 123 72 72 NUM cana-1056 104 124 15 15 NUM cana-1056 104 125 91 91 NUM cana-1056 104 126 32 32 NUM cana-1056 104 127 112 112 NUM cana-1056 104 128 50 50 NUM cana-1056 104 129 92 92 NUM cana-1056 104 130 21 21 NUM cana-1056 104 131 1000 1000 NUM cana-1056 104 132 2 2 NUM cana-1056 104 133 59 59 NUM cana-1056 104 134 20 20 NUM cana-1056 104 135 61 61 NUM cana-1056 104 136 28 28 NUM cana-1056 104 137 59 59 NUM cana-1056 104 138 21 21 NUM cana-1056 104 139 73 73 NUM cana-1056 104 140 32 32 NUM cana-1056 104 141 73 73 NUM cana-1056 105 1 42 42 NUM cana-1056 105 2 71 71 NUM cana-1056 105 3 36 36 NUM cana-1056 105 4 10000 10000 NUM cana-1056 105 5 67 67 NUM cana-1056 105 6 21 21 NUM cana-1056 105 7 73 73 NUM cana-1056 105 8 23 23 NUM cana-1056 105 9 68 68 NUM cana-1056 105 10 21 21 NUM cana-1056 105 11 81 81 NUM cana-1056 105 12 37 37 NUM cana-1056 105 13 91 91 NUM cana-1056 105 14 37 37 NUM cana-1056 105 15 82 82 NUM cana-1056 105 16 36 36 NUM cana-1056 105 17 1000 1000 NUM cana-1056 105 18 3 3 NUM cana-1056 105 19 98 98 NUM cana-1056 105 20 35 35 NUM cana-1056 105 21 106 106 NUM cana-1056 105 22 43 43 NUM cana-1056 105 23 101 101 NUM cana-1056 105 24 35 35 NUM cana-1056 105 25 122 122 NUM cana-1056 105 26 47 47 NUM cana-1056 105 27 122 122 NUM cana-1056 105 28 61 61 NUM cana-1056 105 29 113 113 NUM cana-1056 105 30 47 47 NUM cana-1056 105 31 10000 10000 NUM cana-1056 105 32 60 60 NUM cana-1056 105 33 38 38 NUM cana-1056 105 34 70 70 NUM cana-1056 105 35 45 45 NUM cana-1056 105 36 55 55 NUM cana-1056 105 37 31 31 NUM cana-1056 105 38 83 83 NUM cana-1056 105 39 63 63 NUM cana-1056 105 40 93 93 NUM cana-1056 105 41 65 65 NUM cana-1056 105 42 71 71 NUM cana-1056 105 43 51 51 NUM cana-1056 105 44 1000 1000 NUM cana-1056 105 45 4 4 NUM cana-1056 105 46 69 69 NUM cana-1056 105 47 44 44 NUM cana-1056 105 48 64 64 NUM cana-1056 105 49 39 39 NUM cana-1056 105 50 51 51 NUM cana-1056 105 51 30 30 NUM cana-1056 105 52 93 93 NUM cana-1056 105 53 72 72 NUM cana-1056 105 54 89 89 NUM cana-1056 105 55 53 53 NUM cana-1056 105 56 72 72 NUM cana-1056 105 57 53 53 NUM cana-1056 105 58 10000 10000 NUM cana-1056 105 59 38 38 NUM cana-1056 105 60 18 18 NUM cana-1056 105 61 47 47 NUM cana-1056 105 62 23 23 NUM cana-1056 105 63 41 41 NUM cana-1056 105 64 20 20 NUM cana-1056 105 65 51 51 NUM cana-1056 105 66 39 39 NUM cana-1056 105 67 60 60 NUM cana-1056 105 68 36 36 NUM cana-1056 105 69 54 54 NUM cana-1056 105 70 33 33 NUM cana-1056 105 71 1000 1000 NUM cana-1056 105 72 5 5 NUM cana-1056 105 73 45 45 NUM cana-1056 105 74 20 20 NUM cana-1056 105 75 54 54 NUM cana-1056 105 76 28 28 NUM cana-1056 105 77 49 49 NUM cana-1056 105 78 21 21 NUM cana-1056 105 79 60 60 NUM cana-1056 105 80 34 34 NUM cana-1056 105 81 66 66 NUM cana-1056 105 82 40 40 NUM cana-1056 105 83 61 61 NUM cana-1056 105 84 23 23 NUM cana-1056 105 85 10000 10000 NUM cana-1056 105 86 30 30 NUM cana-1056 105 87 14 14 NUM cana-1056 105 88 30 30 NUM cana-1056 105 89 14 14 NUM cana-1056 105 90 29 29 NUM cana-1056 105 91 15 15 NUM cana-1056 105 92 47 47 NUM cana-1056 105 93 32 32 NUM cana-1056 105 94 47 47 NUM cana-1056 105 95 32 32 NUM cana-1056 105 96 45 45 NUM cana-1056 105 97 27 27 NUM cana-1056 105 98 1000 1000 NUM cana-1056 105 99 6 6 NUM cana-1056 105 100 32 32 NUM cana-1056 105 101 16 16 NUM cana-1056 105 102 32 32 NUM cana-1056 105 103 16 16 NUM cana-1056 105 104 30 30 NUM cana-1056 105 105 15 15 NUM cana-1056 105 106 52 52 NUM cana-1056 105 107 41 41 NUM cana-1056 105 108 52 52 NUM cana-1056 105 109 37 37 NUM cana-1056 105 110 51 51 NUM cana-1056 105 111 41 41 NUM cana-1056 105 112 10000 10000 NUM cana-1056 105 113 102 102 NUM cana-1056 105 114 13 13 NUM cana-1056 105 115 115 115 NUM cana-1056 105 116 15 15 NUM cana-1056 105 117 115 115 NUM cana-1056 105 118 14 14 NUM cana-1056 105 119 153 153 NUM cana-1056 105 120 37 37 NUM cana-1056 105 121 161 161 NUM cana-1056 105 122 43 43 NUM cana-1056 105 123 142 142 NUM cana-1056 105 124 41 41 NUM cana-1056 105 125 1000 1000 NUM cana-1056 105 126 7 7 NUM cana-1056 105 127 90 90 NUM cana-1056 105 128 12 12 NUM cana-1056 105 129 109 109 NUM cana-1056 105 130 14 14 NUM cana-1056 105 131 95 95 NUM cana-1056 105 132 14 14 NUM cana-1056 105 133 104 104 NUM cana-1056 105 134 26 26 NUM cana-1056 105 135 121 121 NUM cana-1056 105 136 28 28 NUM cana-1056 105 137 109 109 NUM cana-1056 105 138 26 26 NUM cana-1056 105 139 10000 10000 NUM cana-1056 105 140 90 90 NUM cana-1056 105 141 11 11 NUM cana-1056 105 142 103 103 NUM cana-1056 105 143 15 15 NUM cana-1056 105 144 99 99 NUM cana-1056 105 145 12 12 NUM cana-1056 105 146 102 102 NUM cana-1056 105 147 23 23 NUM cana-1056 105 148 115 115 NUM cana-1056 105 149 27 27 NUM cana-1056 105 150 111 111 NUM cana-1056 105 151 24 24 NUM cana-1056 105 152 1000 1000 NUM cana-1056 105 153 8 8 NUM cana-1056 105 154 166 166 NUM cana-1056 105 155 15 15 NUM cana-1056 105 156 188 188 NUM cana-1056 105 157 19 19 NUM cana-1056 105 158 178 178 NUM cana-1056 105 159 16 16 NUM cana-1056 105 160 182 182 NUM cana-1056 105 161 29 29 NUM cana-1056 105 162 200 200 NUM cana-1056 105 163 31 31 NUM cana-1056 105 164 192 192 NUM cana-1056 105 165 28 28 NUM cana-1056 105 166 10000 10000 NUM cana-1056 105 167 60 60 NUM cana-1056 105 168 19 19 NUM cana-1056 105 169 129 129 NUM cana-1056 105 170 17 17 NUM cana-1056 105 171 120 120 NUM cana-1056 105 172 15 15 NUM cana-1056 105 173 82 82 NUM cana-1056 105 174 37 37 NUM cana-1056 105 175 152 152 NUM cana-1056 105 176 42 42 NUM cana-1056 105 177 142 142 NUM cana-1056 105 178 41 41 NUM cana-1056 105 179 1000 1000 NUM cana-1056 105 180 9 9 NUM cana-1056 105 181 195 195 NUM cana-1056 105 182 18 18 NUM cana-1056 105 183 200 200 NUM cana-1056 105 184 19 19 NUM cana-1056 105 185 199 199 NUM cana-1056 105 186 19 19 NUM cana-1056 105 187 226 226 NUM cana-1056 105 188 42 42 NUM cana-1056 105 189 302 302 NUM cana-1056 105 190 52 52 NUM cana-1056 105 191 302 302 NUM cana-1056 105 192 52 52 NUM cana-1056 105 193 10000 10000 NUM cana-1056 105 194 95 95 NUM cana-1056 105 195 15 15 NUM cana-1056 105 196 121 121 NUM cana-1056 105 197 17 17 NUM cana-1056 105 198 99 99 NUM cana-1056 105 199 17 17 NUM cana-1056 105 200 107 107 NUM cana-1056 105 201 27 27 NUM cana-1056 105 202 133 133 NUM cana-1056 105 203 29 29 NUM cana-1056 105 204 111 111 NUM cana-1056 105 205 29 29 NUM cana-1056 105 206 1000 1000 NUM cana-1056 105 207 10 10 NUM cana-1056 105 208 163 163 NUM cana-1056 105 209 14 14 NUM cana-1056 105 210 198 198 NUM cana-1056 105 211 21 21 NUM cana-1056 105 212 185 185 NUM cana-1056 105 213 18 18 NUM cana-1056 105 214 182 182 NUM cana-1056 105 215 30 30 NUM cana-1056 105 216 233 233 NUM cana-1056 105 217 47 47 NUM cana-1056 105 218 162 162 NUM cana-1056 105 219 41 41 NUM cana-1056 105 220 10000 10000 NUM cana-1056 105 221 105 105 NUM cana-1056 105 222 32 32 NUM cana-1056 105 223 112 112 NUM cana-1056 105 224 39 39 NUM cana-1056 105 225 108 108 NUM cana-1056 105 226 35 35 NUM cana-1056 105 227 143 143 NUM cana-1056 105 228 52 52 NUM cana-1056 105 229 209 209 NUM cana-1056 105 230 62 62 NUM cana-1056 105 231 142 142 NUM cana-1056 105 232 51 51 NUM cana-1056 105 233 1000 1000 NUM cana-1056 105 234 11 11 NUM cana-1056 105 235 communications communication NOUN cana-1056 105 236 on on ADP cana-1056 105 237 applied apply VERB cana-1056 105 238 nonlinear nonlinear ADJ cana-1056 105 239 analysis analysis NOUN cana-1056 105 240 issn issn NOUN cana-1056 105 241 : : PUNCT cana-1056 105 242 1074 1074 NUM cana-1056 105 243 - - PUNCT cana-1056 105 244 133x 133x NUM cana-1056 105 245 vol vol NOUN cana-1056 105 246 31 31 NUM cana-1056 105 247 no no NOUN cana-1056 105 248 . . PUNCT cana-1056 106 1 5s 5s NUM cana-1056 106 2 ( ( PUNCT cana-1056 106 3 2024 2024 NUM cana-1056 106 4 ) ) PUNCT cana-1056 106 5 379 379 NUM cana-1056 106 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 106 7 133 133 NUM cana-1056 106 8 40 40 NUM cana-1056 106 9 145 145 NUM cana-1056 106 10 45 45 NUM cana-1056 106 11 139 139 NUM cana-1056 106 12 45 45 NUM cana-1056 106 13 145 145 NUM cana-1056 106 14 61 61 NUM cana-1056 106 15 182 182 NUM cana-1056 106 16 61 61 NUM cana-1056 106 17 172 172 NUM cana-1056 106 18 61 61 NUM cana-1056 106 19 10000 10000 NUM cana-1056 106 20 55 55 NUM cana-1056 106 21 23 23 NUM cana-1056 106 22 56 56 NUM cana-1056 106 23 25 25 NUM cana-1056 106 24 55 55 NUM cana-1056 106 25 24 24 NUM cana-1056 106 26 82 82 NUM cana-1056 106 27 51 51 NUM cana-1056 106 28 82 82 NUM cana-1056 106 29 52 52 NUM cana-1056 106 30 82 82 NUM cana-1056 106 31 53 53 NUM cana-1056 106 32 1000 1000 NUM cana-1056 106 33 12 12 NUM cana-1056 106 34 50 50 NUM cana-1056 106 35 20 20 NUM cana-1056 106 36 60 60 NUM cana-1056 106 37 33 33 NUM cana-1056 106 38 51 51 NUM cana-1056 106 39 23 23 NUM cana-1056 106 40 82 82 NUM cana-1056 106 41 44 44 NUM cana-1056 106 42 83 83 NUM cana-1056 106 43 51 51 NUM cana-1056 106 44 83 83 NUM cana-1056 106 45 41 41 NUM cana-1056 106 46 10000 10000 NUM cana-1056 106 47 52 52 NUM cana-1056 106 48 25 25 NUM cana-1056 106 49 66 66 NUM cana-1056 106 50 30 30 NUM cana-1056 106 51 60 60 NUM cana-1056 106 52 25 25 NUM cana-1056 106 53 64 64 NUM cana-1056 106 54 37 37 NUM cana-1056 106 55 78 78 NUM cana-1056 106 56 42 42 NUM cana-1056 106 57 72 72 NUM cana-1056 106 58 37 37 NUM cana-1056 106 59 1000 1000 NUM cana-1056 106 60 13 13 NUM cana-1056 106 61 160 160 NUM cana-1056 106 62 31 31 NUM cana-1056 106 63 191 191 NUM cana-1056 106 64 41 41 NUM cana-1056 106 65 170 170 NUM cana-1056 106 66 38 38 NUM cana-1056 106 67 173 173 NUM cana-1056 106 68 43 43 NUM cana-1056 106 69 203 203 NUM cana-1056 106 70 54 54 NUM cana-1056 106 71 184 184 NUM cana-1056 106 72 50 50 NUM cana-1056 106 73 10000 10000 NUM cana-1056 106 74 80 80 NUM cana-1056 106 75 17 17 NUM cana-1056 106 76 90 90 NUM cana-1056 106 77 35 35 NUM cana-1056 106 78 83 83 NUM cana-1056 106 79 18 18 NUM cana-1056 106 80 92 92 NUM cana-1056 106 81 29 29 NUM cana-1056 106 82 122 122 NUM cana-1056 106 83 52 52 NUM cana-1056 106 84 111 111 NUM cana-1056 106 85 41 41 NUM cana-1056 106 86 1000 1000 NUM cana-1056 106 87 14 14 NUM cana-1056 106 88 70 70 NUM cana-1056 106 89 12 12 NUM cana-1056 106 90 77 77 NUM cana-1056 106 91 20 20 NUM cana-1056 106 92 77 77 NUM cana-1056 106 93 20 20 NUM cana-1056 106 94 102 102 NUM cana-1056 106 95 34 34 NUM cana-1056 106 96 103 103 NUM cana-1056 106 97 41 41 NUM cana-1056 106 98 103 103 NUM cana-1056 106 99 41 41 NUM cana-1056 106 100 10000 10000 NUM cana-1056 106 101 80 80 NUM cana-1056 106 102 17 17 NUM cana-1056 106 103 90 90 NUM cana-1056 106 104 35 35 NUM cana-1056 106 105 83 83 NUM cana-1056 106 106 18 18 NUM cana-1056 106 107 83 83 NUM cana-1056 106 108 31 31 NUM cana-1056 106 109 92 92 NUM cana-1056 106 110 41 41 NUM cana-1056 106 111 101 101 NUM cana-1056 106 112 30 30 NUM cana-1056 106 113 1000 1000 NUM cana-1056 106 114 15 15 NUM cana-1056 106 115 100 100 NUM cana-1056 106 116 58 58 NUM cana-1056 106 117 106 106 NUM cana-1056 106 118 70 70 NUM cana-1056 106 119 102 102 NUM cana-1056 106 120 60 60 NUM cana-1056 106 121 122 122 NUM cana-1056 106 122 70 70 NUM cana-1056 106 123 126 126 NUM cana-1056 106 124 83 83 NUM cana-1056 106 125 120 120 NUM cana-1056 106 126 81 81 NUM cana-1056 106 127 10000 10000 NUM cana-1056 106 128 94 94 NUM cana-1056 106 129 11 11 NUM cana-1056 106 130 100 100 NUM cana-1056 106 131 14 14 NUM cana-1056 106 132 98 98 NUM cana-1056 106 133 13 13 NUM cana-1056 106 134 106 106 NUM cana-1056 106 135 25 25 NUM cana-1056 106 136 112 112 NUM cana-1056 106 137 26 26 NUM cana-1056 106 138 110 110 NUM cana-1056 106 139 27 27 NUM cana-1056 106 140 1000 1000 NUM cana-1056 106 141 16 16 NUM cana-1056 106 142 94 94 NUM cana-1056 106 143 16 16 NUM cana-1056 106 144 109 109 NUM cana-1056 106 145 14 14 NUM cana-1056 106 146 109 109 NUM cana-1056 106 147 19 19 NUM cana-1056 106 148 106 106 NUM cana-1056 106 149 30 30 NUM cana-1056 106 150 121 121 NUM cana-1056 106 151 26 26 NUM cana-1056 106 152 122 122 NUM cana-1056 106 153 31 31 NUM cana-1056 106 154 10000 10000 NUM cana-1056 106 155 2753 2753 NUM cana-1056 106 156 710 710 NUM cana-1056 106 157 3140 3140 NUM cana-1056 106 158 874 874 NUM cana-1056 106 159 2937 2937 NUM cana-1056 106 160 743 743 NUM cana-1056 106 161 3416 3416 NUM cana-1056 106 162 1288 1288 NUM cana-1056 106 163 3965 3965 NUM cana-1056 106 164 1448 1448 NUM cana-1056 106 165 3720 3720 NUM cana-1056 106 166 1317 1317 NUM cana-1056 106 167 total total NOUN cana-1056 106 168 clearly clearly ADV cana-1056 106 169 , , PUNCT cana-1056 106 170 we we PRON cana-1056 106 171 have have VERB cana-1056 106 172 from from ADP cana-1056 106 173 the the DET cana-1056 106 174 table table NOUN cana-1056 106 175 ( ( PUNCT cana-1056 106 176 2 2 NUM cana-1056 106 177 ) ) PUNCT cana-1056 106 178 that that SCONJ cana-1056 106 179 new1algorithm new1algorithm PROPN cana-1056 106 180 beats beat VERB cana-1056 106 181 ( ( PUNCT cana-1056 106 182 hs hs NOUN cana-1056 106 183 ) ) PUNCT cana-1056 106 184 algorithm algorithm NOUN cana-1056 106 185 in in ADP cana-1056 106 186 about about ADP cana-1056 106 187 ( ( PUNCT cana-1056 106 188 44 44 NUM cana-1056 106 189 % % NOUN cana-1056 106 190 ) ) PUNCT cana-1056 106 191 noi noi PROPN cana-1056 106 192 ; ; PUNCT cana-1056 106 193 ( ( PUNCT cana-1056 106 194 21 21 NUM cana-1056 106 195 % % NOUN cana-1056 106 196 ) ) PUNCT cana-1056 106 197 nof nof PROPN cana-1056 106 198 , , PUNCT cana-1056 106 199 also also ADV cana-1056 106 200 , , PUNCT cana-1056 106 201 we we PRON cana-1056 106 202 have have VERB cana-1056 106 203 the the DET cana-1056 106 204 new2 new2 ADJ cana-1056 106 205 algorithm algorithm NOUN cana-1056 106 206 beats beat NOUN cana-1056 106 207 ( ( PUNCT cana-1056 106 208 pr pr NOUN cana-1056 106 209 ) ) PUNCT cana-1056 106 210 algorithm algorithm NOUN cana-1056 106 211 in in ADP cana-1056 106 212 about about ADP cana-1056 106 213 ( ( PUNCT cana-1056 106 214 40 40 NUM cana-1056 106 215 % % NOUN cana-1056 106 216 ) ) PUNCT cana-1056 107 1 noi,(21 noi,(21 ADV cana-1056 107 2 % % NOUN cana-1056 107 3 ) ) PUNCT cana-1056 108 1 nof nof NOUN cana-1056 108 2 then then ADV cana-1056 108 3 we we PRON cana-1056 108 4 have have VERB cana-1056 108 5 the the DET cana-1056 108 6 new3 new3 ADJ cana-1056 108 7 algorithm algorithm NOUN cana-1056 108 8 beats beat NOUN cana-1056 108 9 ( ( PUNCT cana-1056 108 10 ls ls ADJ cana-1056 108 11 ) ) PUNCT cana-1056 108 12 algorithm algorithm NOUN cana-1056 108 13 in in ADP cana-1056 108 14 about about ADP cana-1056 108 15 ( ( PUNCT cana-1056 108 16 45 45 NUM cana-1056 108 17 % % NOUN cana-1056 108 18 ) ) PUNCT cana-1056 108 19 noi,(19 noi,(19 NUM cana-1056 108 20 % % NOUN cana-1056 108 21 ) ) PUNCT cana-1056 108 22 nof nof PROPN cana-1056 108 23 . . PUNCT cana-1056 109 1 table2 table2 NOUN cana-1056 109 2 : : PUNCT cana-1056 109 3 percentage percentage NOUN cana-1056 109 4 modified modify VERB cana-1056 109 5 of of ADP cana-1056 109 6 the the DET cana-1056 109 7 new new ADJ cana-1056 109 8 algorthims algorthim NOUN cana-1056 109 9 hs hs PROPN cana-1056 109 10 algorithm algorithm PROPN cana-1056 109 11 𝛽𝑁1 𝛽𝑁1 PROPN cana-1056 109 12 pr pr NOUN cana-1056 109 13 algorithm algorithm NOUN cana-1056 109 14 𝛽𝑁2 𝛽𝑁2 ADP cana-1056 109 15 ls ls ADJ cana-1056 109 16 algorithm algorithm NOUN cana-1056 109 17 𝛽𝑁3 𝛽𝑁3 VERB cana-1056 109 18 ni ni PROPN cana-1056 109 19 100 100 NUM cana-1056 109 20 % % NOUN cana-1056 109 21 56 56 NUM cana-1056 109 22 % % NOUN cana-1056 109 23 100 100 NUM cana-1056 109 24 % % NOUN cana-1056 109 25 60 60 NUM cana-1056 109 26 % % NOUN cana-1056 109 27 100 100 NUM cana-1056 109 28 % % NOUN cana-1056 109 29 55 55 NUM cana-1056 109 30 % % NOUN cana-1056 109 31 nf nf NOUN cana-1056 109 32 100 100 NUM cana-1056 109 33 % % NOUN cana-1056 109 34 79 79 NUM cana-1056 109 35 % % NOUN cana-1056 109 36 100 100 NUM cana-1056 109 37 % % NOUN cana-1056 109 38 79 79 NUM cana-1056 109 39 % % NOUN cana-1056 109 40 100 100 NUM cana-1056 109 41 % % NOUN cana-1056 109 42 81 81 NUM cana-1056 109 43 % % NOUN cana-1056 109 44 the the DET cana-1056 109 45 charts chart NOUN cana-1056 109 46 below below ADP cana-1056 109 47 ( ( PUNCT cana-1056 109 48 fig(1 fig(1 NOUN cana-1056 109 49 ) ) PUNCT cana-1056 109 50 , , PUNCT cana-1056 109 51 fig(2 fig(2 NOUN cana-1056 109 52 ) ) PUNCT cana-1056 109 53 ( ( PUNCT cana-1056 109 54 show show VERB cana-1056 109 55 the the DET cana-1056 109 56 comparison comparison NOUN cana-1056 109 57 of of ADP cana-1056 109 58 the the DET cana-1056 109 59 new new ADJ cana-1056 109 60 algorithm algorithm NOUN cana-1056 109 61 with with ADP cana-1056 109 62 similar similar ADJ cana-1056 109 63 algorithms algorithm NOUN cana-1056 109 64 ( ( PUNCT cana-1056 109 65 hs hs INTJ cana-1056 109 66 , , PUNCT cana-1056 109 67 pr pr NOUN cana-1056 109 68 , , PUNCT cana-1056 109 69 ls ls PROPN cana-1056 109 70 ) ) PUNCT cana-1056 109 71 based base VERB cana-1056 109 72 on on ADP cana-1056 109 73 the the DET cana-1056 109 74 number number NOUN cana-1056 109 75 of of ADP cana-1056 109 76 iterations iteration NOUN cana-1056 109 77 and and CCONJ cana-1056 109 78 the the DET cana-1056 109 79 number number NOUN cana-1056 109 80 of of ADP cana-1056 109 81 function function NOUN cana-1056 109 82 calculations calculation NOUN cana-1056 109 83 , , PUNCT cana-1056 109 84 respectively respectively ADV cana-1056 109 85 . . PUNCT cana-1056 110 1 we we PRON cana-1056 110 2 used use VERB cana-1056 110 3 more more ADJ cana-1056 110 4 , , PUNCT cana-1056 110 5 dolan dolan PROPN cana-1056 110 6 to to PART cana-1056 110 7 compare compare VERB cana-1056 110 8 the the DET cana-1056 110 9 new new ADJ cana-1056 110 10 methods method NOUN cana-1056 110 11 with with ADP cana-1056 110 12 the the DET cana-1056 110 13 classical classical ADJ cana-1056 110 14 methods method NOUN cana-1056 110 15 , , PUNCT cana-1056 110 16 based base VERB cana-1056 110 17 on on ADP cana-1056 110 18 the the DET cana-1056 110 19 number number NOUN cana-1056 110 20 of of ADP cana-1056 110 21 iterations iteration NOUN cana-1056 110 22 and and CCONJ cana-1056 110 23 the the DET cana-1056 110 24 number number NOUN cana-1056 110 25 of of ADP cana-1056 110 26 function function NOUN cana-1056 110 27 calculations calculation NOUN cana-1056 110 28 . . PUNCT cana-1056 111 1 figure figure VERB cana-1056 111 2 1 1 NUM cana-1056 111 3 : : PUNCT cana-1056 111 4 number number NOUN cana-1056 111 5 of of ADP cana-1056 111 6 iteration iteration NOUN cana-1056 111 7 comparing compare VERB cana-1056 111 8 bewteen bewteen VERB cana-1056 111 9 new new ADJ cana-1056 111 10 methods method NOUN cana-1056 111 11 to to PART cana-1056 111 12 standred standre VERB cana-1056 111 13 methods method NOUN cana-1056 111 14 figure figure VERB cana-1056 111 15 2 2 NUM cana-1056 111 16 : : PUNCT cana-1056 111 17 number number NOUN cana-1056 111 18 of of ADP cana-1056 111 19 function function NOUN cana-1056 111 20 evaluation evaluation NOUN cana-1056 111 21 comparing compare VERB cana-1056 111 22 bewteen bewteen VERB cana-1056 111 23 new new ADJ cana-1056 111 24 methods method NOUN cana-1056 111 25 to to PART cana-1056 111 26 standred standre VERB cana-1056 111 27 method method NOUN cana-1056 111 28 communications communication NOUN cana-1056 111 29 on on ADP cana-1056 111 30 applied apply VERB cana-1056 111 31 nonlinear nonlinear ADJ cana-1056 111 32 analysis analysis NOUN cana-1056 111 33 issn issn NOUN cana-1056 111 34 : : PUNCT cana-1056 111 35 1074 1074 NUM cana-1056 111 36 - - PUNCT cana-1056 111 37 133x 133x NUM cana-1056 111 38 vol vol NOUN cana-1056 111 39 31 31 NUM cana-1056 111 40 no no NOUN cana-1056 111 41 . . PUNCT cana-1056 112 1 5s 5s NUM cana-1056 112 2 ( ( PUNCT cana-1056 112 3 2024 2024 NUM cana-1056 112 4 ) ) PUNCT cana-1056 112 5 380 380 NUM cana-1056 112 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 112 7 5 5 NUM cana-1056 112 8 . . PUNCT cana-1056 112 9 conclusion conclusion NOUN cana-1056 112 10 1 1 NUM cana-1056 112 11 . . PUNCT cana-1056 113 1 the the DET cana-1056 113 2 cg cg NOUN cana-1056 113 3 methods method NOUN cana-1056 113 4 are be AUX cana-1056 113 5 proposed propose VERB cana-1056 113 6 for for ADP cana-1056 113 7 solving solve VERB cana-1056 113 8 nonlinear nonlinear ADJ cana-1056 113 9 optimization optimization NOUN cana-1056 113 10 problems problem NOUN cana-1056 113 11 2 2 NUM cana-1056 113 12 . . NOUN cana-1056 113 13 adequate adequate ADJ cana-1056 113 14 decrease decrease NOUN cana-1056 113 15 and and CCONJ cana-1056 113 16 worldwide worldwide ADJ cana-1056 113 17 convergence convergence NOUN cana-1056 113 18 can can AUX cana-1056 113 19 be be AUX cana-1056 113 20 achieved achieve VERB cana-1056 113 21 under under ADP cana-1056 113 22 certain certain ADJ cana-1056 113 23 conditions condition NOUN cana-1056 113 24 . . PUNCT cana-1056 114 1 the the DET cana-1056 114 2 numerical numerical ADJ cana-1056 114 3 findings finding NOUN cana-1056 114 4 shown show VERB cana-1056 114 5 in in ADP cana-1056 114 6 the the DET cana-1056 114 7 previously previously ADV cana-1056 114 8 mentioned mention VERB cana-1056 114 9 figure figure NOUN cana-1056 114 10 . . PUNCT cana-1056 115 1 3.the 3.the DET cana-1056 115 2 new new ADJ cana-1056 115 3 algorithms algorithm NOUN cana-1056 115 4 ( ( PUNCT cana-1056 115 5 𝛽𝑁1 𝛽𝑁1 PROPN cana-1056 115 6 , , PUNCT cana-1056 115 7 𝛽𝑁2 𝛽𝑁2 ADJ cana-1056 115 8 , , PUNCT cana-1056 115 9 𝛽𝑁3 𝛽𝑁3 PROPN cana-1056 115 10 ) ) PUNCT cana-1056 115 11 have have AUX cana-1056 115 12 prove prove VERB cana-1056 115 13 its its PRON cana-1056 115 14 efficiency efficiency NOUN cana-1056 115 15 through through ADP cana-1056 115 16 results result NOUN cana-1056 115 17 in in ADP cana-1056 115 18 table(1 table(1 NOUN cana-1056 115 19 ) ) PUNCT cana-1056 115 20 and(2 and(2 NOUN cana-1056 115 21 ) ) PUNCT cana-1056 115 22 references reference NOUN cana-1056 115 23 [ [ X cana-1056 115 24 1 1 NUM cana-1056 115 25 ] ] X cana-1056 115 26 y. y. PROPN cana-1056 115 27 liu liu PROPN cana-1056 115 28 and and CCONJ cana-1056 115 29 c. c. PROPN cana-1056 115 30 storey storey PROPN cana-1056 115 31 , , PUNCT cana-1056 115 32 β€œ " PUNCT cana-1056 115 33 efficient efficient ADJ cana-1056 115 34 generalized generalize VERB cana-1056 115 35 conjugate conjugate ADJ cana-1056 115 36 gradient gradient ADJ cana-1056 115 37 algorithms algorithm NOUN cana-1056 115 38 , , PUNCT cana-1056 115 39 part part NOUN cana-1056 115 40 1 1 NUM cana-1056 115 41 : : PUNCT cana-1056 115 42 theory theory NOUN cana-1056 115 43 , , PUNCT cana-1056 115 44 ” " PUNCT cana-1056 115 45 j. j. PROPN cana-1056 115 46 optim optim PROPN cana-1056 115 47 . . PUNCT cana-1056 116 1 theory theory NOUN cana-1056 116 2 appl appl PROPN cana-1056 116 3 . . PROPN cana-1056 117 1 , , PUNCT cana-1056 117 2 vol vol NOUN cana-1056 117 3 . . PROPN cana-1056 118 1 69 69 NUM cana-1056 118 2 , , PUNCT cana-1056 118 3 pp pp ADJ cana-1056 118 4 . . PUNCT cana-1056 119 1 129–137 129–137 NUM cana-1056 119 2 , , PUNCT cana-1056 119 3 1991 1991 NUM cana-1056 119 4 . . PUNCT cana-1056 120 1 [ [ X cana-1056 120 2 2 2 X cana-1056 120 3 ] ] PUNCT cana-1056 120 4 e. e. PROPN cana-1056 120 5 polak polak PROPN cana-1056 120 6 and and CCONJ cana-1056 120 7 g. g. PROPN cana-1056 120 8 ribiere ribiere PROPN cana-1056 120 9 , , PUNCT cana-1056 120 10 β€œ " PUNCT cana-1056 120 11 note note VERB cana-1056 120 12 sur sur PROPN cana-1056 120 13 la la X cana-1056 120 14 convergence convergence PROPN cana-1056 120 15 de de X cana-1056 120 16 mΓ©thodes mΓ©thodes PROPN cana-1056 120 17 de de PROPN cana-1056 120 18 directions direction NOUN cana-1056 120 19 conjuguΓ©es conjuguΓ©es PROPN cana-1056 120 20 , , PUNCT cana-1056 120 21 ” " PUNCT cana-1056 120 22 rev rev X cana-1056 120 23 . . PROPN cana-1056 120 24 franΓ§aise franΓ§aise PROPN cana-1056 120 25 d’informatique d’informatique PROPN cana-1056 120 26 rech rech NOUN cana-1056 120 27 . . PUNCT cana-1056 121 1 opΓ©rationnelle opΓ©rationnelle PROPN cana-1056 121 2 . . PUNCT cana-1056 122 1 sΓ©rie sΓ©rie PROPN cana-1056 122 2 rouge rouge PROPN cana-1056 122 3 , , PUNCT cana-1056 122 4 vol vol NOUN cana-1056 122 5 . . PROPN cana-1056 123 1 3 3 NUM cana-1056 123 2 , , PUNCT cana-1056 123 3 no no INTJ cana-1056 123 4 . . NOUN cana-1056 123 5 16 16 NUM cana-1056 123 6 , , PUNCT cana-1056 123 7 pp pp ADJ cana-1056 123 8 . . PUNCT cana-1056 124 1 35–43 35–43 NUM cana-1056 124 2 , , PUNCT cana-1056 124 3 1969 1969 NUM cana-1056 124 4 . . PUNCT cana-1056 125 1 [ [ X cana-1056 125 2 3 3 X cana-1056 125 3 ] ] X cana-1056 125 4 e. e. PROPN cana-1056 125 5 stiefel stiefel PROPN cana-1056 125 6 , , PUNCT cana-1056 125 7 β€œ " PUNCT cana-1056 125 8 methods method NOUN cana-1056 125 9 of of ADP cana-1056 125 10 conjugate conjugate ADJ cana-1056 125 11 gradients gradient NOUN cana-1056 125 12 for for ADP cana-1056 125 13 solving solve VERB cana-1056 125 14 linear linear NOUN cana-1056 125 15 systems system NOUN cana-1056 125 16 , , PUNCT cana-1056 125 17 ” " PUNCT cana-1056 125 18 j. j. PROPN cana-1056 125 19 res res PROPN cana-1056 125 20 . . PUNCT cana-1056 126 1 nat nat PROPN cana-1056 126 2 . . PUNCT cana-1056 127 1 bur bur PROPN cana-1056 127 2 . . PUNCT cana-1056 128 1 stand stand VERB cana-1056 128 2 . . PUNCT cana-1056 129 1 , , PUNCT cana-1056 129 2 vol vol NOUN cana-1056 129 3 . . PROPN cana-1056 129 4 49 49 NUM cana-1056 129 5 , , PUNCT cana-1056 129 6 pp pp ADJ cana-1056 129 7 . . PUNCT cana-1056 130 1 409 409 NUM cana-1056 130 2 – – PUNCT cana-1056 130 3 435 435 NUM cana-1056 130 4 , , PUNCT cana-1056 130 5 1952 1952 NUM cana-1056 130 6 . . PUNCT cana-1056 131 1 [ [ X cana-1056 131 2 4 4 X cana-1056 131 3 ] ] X cana-1056 131 4 s. s. PROPN cana-1056 131 5 bojari bojari PROPN cana-1056 131 6 and and CCONJ cana-1056 131 7 m. m. PROPN cana-1056 131 8 r. r. PROPN cana-1056 131 9 eslahchi eslahchi PROPN cana-1056 131 10 , , PUNCT cana-1056 131 11 β€œ " PUNCT cana-1056 131 12 global global ADJ cana-1056 131 13 convergence convergence NOUN cana-1056 131 14 of of ADP cana-1056 131 15 a a DET cana-1056 131 16 family family NOUN cana-1056 131 17 of of ADP cana-1056 131 18 modified modify VERB cana-1056 131 19 bfgs bfgs ADJ cana-1056 131 20 methods method NOUN cana-1056 131 21 under under ADP cana-1056 131 22 a a DET cana-1056 131 23 modified modify VERB cana-1056 131 24 weakwolfe weakwolfe NOUN cana-1056 131 25 – – PUNCT cana-1056 131 26 powell powell PROPN cana-1056 131 27 line line NOUN cana-1056 131 28 search search NOUN cana-1056 131 29 for for ADP cana-1056 131 30 nonconvex nonconvex NOUN cana-1056 131 31 functions function NOUN cana-1056 131 32 , , PUNCT cana-1056 131 33 ” " PUNCT cana-1056 131 34 4or 4or ADJ cana-1056 131 35 , , PUNCT cana-1056 131 36 vol vol NOUN cana-1056 131 37 . . PROPN cana-1056 131 38 18 18 NUM cana-1056 131 39 , , PUNCT cana-1056 131 40 no no INTJ cana-1056 131 41 . . NOUN cana-1056 131 42 2 2 NUM cana-1056 131 43 , , PUNCT cana-1056 131 44 pp pp ADJ cana-1056 131 45 . . PUNCT cana-1056 132 1 219–244 219–244 NUM cana-1056 132 2 , , PUNCT cana-1056 132 3 2020 2020 NUM cana-1056 132 4 . . PUNCT cana-1056 133 1 [ [ X cana-1056 133 2 5 5 X cana-1056 133 3 ] ] PUNCT cana-1056 133 4 j. j. PROPN cana-1056 133 5 nocedal nocedal PROPN cana-1056 133 6 and and CCONJ cana-1056 133 7 s. s. PROPN cana-1056 133 8 j. j. PROPN cana-1056 133 9 wright wright PROPN cana-1056 133 10 , , PUNCT cana-1056 133 11 numerical numerical PROPN cana-1056 133 12 optimization optimization NOUN cana-1056 133 13 . . PUNCT cana-1056 134 1 springer springer NOUN cana-1056 134 2 , , PUNCT cana-1056 134 3 1999 1999 NUM cana-1056 134 4 . . PUNCT cana-1056 135 1 [ [ X cana-1056 135 2 6 6 NUM cana-1056 135 3 ] ] PUNCT cana-1056 135 4 h. h. PROPN cana-1056 135 5 a. a. PROPN cana-1056 135 6 khatab khatab PROPN cana-1056 135 7 and and CCONJ cana-1056 135 8 s. s. PROPN cana-1056 135 9 g. g. PROPN cana-1056 135 10 sharef sharef PROPN cana-1056 135 11 , , PUNCT cana-1056 135 12 β€œ " PUNCT cana-1056 135 13 a a DET cana-1056 135 14 new new ADJ cana-1056 135 15 modified modify VERB cana-1056 135 16 conjugate conjugate ADJ cana-1056 135 17 gradient gradient NOUN cana-1056 135 18 for for ADP cana-1056 135 19 nonlinear nonlinear ADJ cana-1056 135 20 minimization minimization NOUN cana-1056 135 21 problems problem NOUN cana-1056 135 22 , , PUNCT cana-1056 135 23 ” " PUNCT cana-1056 135 24 sci sci PROPN cana-1056 135 25 . . PUNCT cana-1056 136 1 j. j. PROPN cana-1056 136 2 univ univ PROPN cana-1056 136 3 . . PUNCT cana-1056 137 1 zakho zakho PROPN cana-1056 137 2 , , PUNCT cana-1056 137 3 vol vol NOUN cana-1056 137 4 . . PROPN cana-1056 138 1 10 10 NUM cana-1056 138 2 , , PUNCT cana-1056 138 3 no no INTJ cana-1056 138 4 . . NOUN cana-1056 138 5 4 4 NUM cana-1056 138 6 , , PUNCT cana-1056 138 7 pp pp ADJ cana-1056 138 8 . . PUNCT cana-1056 139 1 169–174 169–174 NUM cana-1056 139 2 , , PUNCT cana-1056 139 3 2022 2022 NUM cana-1056 139 4 . . PUNCT cana-1056 140 1 [ [ X cana-1056 140 2 7 7 X cana-1056 140 3 ] ] PUNCT cana-1056 140 4 j. j. PROPN cana-1056 140 5 zhang zhang PROPN cana-1056 140 6 and and CCONJ cana-1056 140 7 c. c. PROPN cana-1056 140 8 xu xu PROPN cana-1056 140 9 , , PUNCT cana-1056 140 10 β€œ " PUNCT cana-1056 140 11 properties property NOUN cana-1056 140 12 and and CCONJ cana-1056 140 13 numerical numerical ADJ cana-1056 140 14 performance performance NOUN cana-1056 140 15 of of ADP cana-1056 140 16 quasi quasi ADJ cana-1056 140 17 - - ADJ cana-1056 140 18 newton newton PROPN cana-1056 140 19 methods method NOUN cana-1056 140 20 with with ADP cana-1056 140 21 modified modified ADJ cana-1056 140 22 quasi quasi PROPN cana-1056 140 23 - - PROPN cana-1056 140 24 newton newton PROPN cana-1056 140 25 equations equation NOUN cana-1056 140 26 , , PUNCT cana-1056 140 27 ” " PUNCT cana-1056 140 28 j. j. PROPN cana-1056 140 29 comput comput PROPN cana-1056 140 30 . . PUNCT cana-1056 141 1 appl appl PROPN cana-1056 141 2 . . PROPN cana-1056 141 3 math math PROPN cana-1056 141 4 . . PUNCT cana-1056 142 1 , , PUNCT cana-1056 142 2 vol vol NOUN cana-1056 142 3 . . PROPN cana-1056 143 1 137 137 NUM cana-1056 143 2 , , PUNCT cana-1056 143 3 no no INTJ cana-1056 143 4 . . NOUN cana-1056 143 5 2 2 NUM cana-1056 143 6 , , PUNCT cana-1056 143 7 pp pp ADJ cana-1056 143 8 . . PUNCT cana-1056 144 1 269–278 269–278 NUM cana-1056 144 2 , , PUNCT cana-1056 144 3 2001 2001 NUM cana-1056 144 4 . . PUNCT cana-1056 145 1 [ [ X cana-1056 145 2 8 8 NUM cana-1056 145 3 ] ] PUNCT cana-1056 145 4 a. a. NOUN cana-1056 145 5 a. a. PROPN cana-1056 145 6 hassan hassan PROPN cana-1056 145 7 and and CCONJ cana-1056 145 8 h. h. PROPN cana-1056 145 9 t. t. PROPN cana-1056 145 10 saeed saeed PROPN cana-1056 145 11 , , PUNCT cana-1056 145 12 β€œ " PUNCT cana-1056 145 13 the the DET cana-1056 145 14 modification modification NOUN cana-1056 145 15 conjugate conjugate ADJ cana-1056 145 16 coefficient coefficient NOUN cana-1056 145 17 for for ADP cana-1056 145 18 conjugate conjugate ADJ cana-1056 145 19 gradient gradient NOUN cana-1056 145 20 method method NOUN cana-1056 145 21 to to ADP cana-1056 145 22 solving solve VERB cana-1056 145 23 unconstrained unconstrained ADJ cana-1056 145 24 optimization optimization NOUN cana-1056 145 25 problems problem NOUN cana-1056 145 26 , , PUNCT cana-1056 145 27 ” " PUNCT cana-1056 145 28 in in ADP cana-1056 145 29 bio bio PROPN cana-1056 145 30 web web NOUN cana-1056 145 31 of of ADP cana-1056 145 32 conferences conference NOUN cana-1056 145 33 , , PUNCT cana-1056 145 34 edp edp NOUN cana-1056 145 35 sciences science NOUN cana-1056 145 36 , , PUNCT cana-1056 145 37 2024 2024 NUM cana-1056 145 38 , , PUNCT cana-1056 145 39 p. p. NOUN cana-1056 145 40 143 143 NUM cana-1056 145 41 . . PUNCT cana-1056 146 1 [ [ X cana-1056 146 2 9 9 NUM cana-1056 146 3 ] ] PUNCT cana-1056 146 4 y.-h y.-h NOUN cana-1056 146 5 . . PUNCT cana-1056 147 1 dai dai PROPN cana-1056 147 2 and and CCONJ cana-1056 147 3 l.-z l.-z PROPN cana-1056 147 4 . . PUNCT cana-1056 148 1 liao liao PROPN cana-1056 148 2 , , PUNCT cana-1056 148 3 β€œ " PUNCT cana-1056 148 4 new new ADJ cana-1056 148 5 conjugacy conjugacy ADJ cana-1056 148 6 conditions condition NOUN cana-1056 148 7 and and CCONJ cana-1056 148 8 related relate VERB cana-1056 148 9 nonlinear nonlinear ADJ cana-1056 148 10 conjugate conjugate ADJ cana-1056 148 11 gradient gradient ADJ cana-1056 148 12 methods method NOUN cana-1056 148 13 , , PUNCT cana-1056 148 14 ” " PUNCT cana-1056 148 15 appl appl NOUN cana-1056 148 16 . . PROPN cana-1056 148 17 math math PROPN cana-1056 148 18 . . PUNCT cana-1056 149 1 optim optim PROPN cana-1056 149 2 . . PROPN cana-1056 149 3 , , PUNCT cana-1056 149 4 vol vol NOUN cana-1056 149 5 . . PROPN cana-1056 149 6 1 1 NUM cana-1056 149 7 , , PUNCT cana-1056 149 8 no no INTJ cana-1056 149 9 . . NOUN cana-1056 149 10 43 43 NUM cana-1056 149 11 , , PUNCT cana-1056 149 12 pp pp ADJ cana-1056 149 13 . . PUNCT cana-1056 150 1 87–101 87–101 NUM cana-1056 150 2 , , PUNCT cana-1056 150 3 2001 2001 NUM cana-1056 150 4 . . PUNCT cana-1056 151 1 [ [ X cana-1056 151 2 10 10 NUM cana-1056 151 3 ] ] X cana-1056 151 4 h. h. PROPN cana-1056 151 5 yabe yabe PROPN cana-1056 151 6 and and CCONJ cana-1056 151 7 m. m. PROPN cana-1056 151 8 takano takano PROPN cana-1056 151 9 , , PUNCT cana-1056 151 10 β€œ " PUNCT cana-1056 151 11 global global ADJ cana-1056 151 12 convergence convergence NOUN cana-1056 151 13 properties property NOUN cana-1056 151 14 of of ADP cana-1056 151 15 nonlinear nonlinear ADJ cana-1056 151 16 conjugate conjugate ADJ cana-1056 151 17 gradient gradient ADJ cana-1056 151 18 methods method NOUN cana-1056 151 19 with with ADP cana-1056 151 20 modified modified ADJ cana-1056 151 21 secant secant ADJ cana-1056 151 22 condition condition NOUN cana-1056 151 23 , , PUNCT cana-1056 151 24 ” " PUNCT cana-1056 151 25 comput comput NOUN cana-1056 151 26 . . PUNCT cana-1056 152 1 optim optim PROPN cana-1056 152 2 . . PUNCT cana-1056 153 1 appl appl PROPN cana-1056 153 2 . . PROPN cana-1056 153 3 , , PUNCT cana-1056 153 4 vol vol NOUN cana-1056 153 5 . . PROPN cana-1056 153 6 28 28 NUM cana-1056 153 7 , , PUNCT cana-1056 153 8 no no INTJ cana-1056 153 9 . . NOUN cana-1056 153 10 2 2 NUM cana-1056 153 11 , , PUNCT cana-1056 153 12 pp pp ADJ cana-1056 153 13 . . PUNCT cana-1056 154 1 203–225 203–225 NUM cana-1056 154 2 , , PUNCT cana-1056 154 3 2004 2004 NUM cana-1056 154 4 , , PUNCT cana-1056 154 5 doi doi NOUN cana-1056 154 6 : : PUNCT cana-1056 154 7 10.1023 10.1023 NUM cana-1056 154 8 / / SYM cana-1056 154 9 b b NOUN cana-1056 154 10 : : PUNCT cana-1056 154 11 coap.0000026885.81997.88 coap.0000026885.81997.88 PROPN cana-1056 154 12 . . PUNCT cana-1056 155 1 [ [ X cana-1056 155 2 11 11 NUM cana-1056 155 3 ] ] PUNCT cana-1056 155 4 m. m. NOUN cana-1056 155 5 javad javad PROPN cana-1056 155 6 ebadi ebadi PROPN cana-1056 155 7 , , PUNCT cana-1056 155 8 a. a. NOUN cana-1056 155 9 fahs fah NOUN cana-1056 155 10 , , PUNCT cana-1056 155 11 h. h. PROPN cana-1056 155 12 fahs fah NOUN cana-1056 155 13 , , PUNCT cana-1056 155 14 and and CCONJ cana-1056 155 15 r. r. PROPN cana-1056 155 16 dehghani dehghani PROPN cana-1056 155 17 , , PUNCT cana-1056 155 18 β€œ " PUNCT cana-1056 155 19 competitive competitive ADJ cana-1056 155 20 secant secant ADJ cana-1056 155 21 ( ( PUNCT cana-1056 155 22 bfgs bfgs ADJ cana-1056 155 23 ) ) PUNCT cana-1056 155 24 methods method NOUN cana-1056 155 25 based base VERB cana-1056 155 26 on on ADP cana-1056 155 27 modified modified ADJ cana-1056 155 28 secant secant ADJ cana-1056 155 29 relations relation NOUN cana-1056 155 30 for for ADP cana-1056 155 31 unconstrained unconstrained ADJ cana-1056 155 32 optimization optimization NOUN cana-1056 155 33 , , PUNCT cana-1056 155 34 ” " PUNCT cana-1056 155 35 optimization optimization NOUN cana-1056 155 36 , , PUNCT cana-1056 155 37 vol vol NOUN cana-1056 155 38 . . PROPN cana-1056 155 39 72 72 NUM cana-1056 155 40 , , PUNCT cana-1056 155 41 no no INTJ cana-1056 155 42 . . NOUN cana-1056 155 43 7 7 NUM cana-1056 155 44 , , PUNCT cana-1056 155 45 pp pp ADJ cana-1056 155 46 . . PUNCT cana-1056 155 47 1691–1706 1691–1706 NUM cana-1056 155 48 , , PUNCT cana-1056 155 49 2023 2023 NUM cana-1056 155 50 . . PUNCT cana-1056 156 1 [ [ X cana-1056 156 2 12 12 NUM cana-1056 156 3 ] ] X cana-1056 156 4 s. s. PROPN cana-1056 156 5 g. g. PROPN cana-1056 156 6 shareef shareef PROPN cana-1056 156 7 , , PUNCT cana-1056 156 8 β€œ " PUNCT cana-1056 156 9 a a DET cana-1056 156 10 descent descent NOUN cana-1056 156 11 conjugate conjugate VERB cana-1056 156 12 gradient gradient NOUN cana-1056 156 13 method method NOUN cana-1056 156 14 with with ADP cana-1056 156 15 global global ADJ cana-1056 156 16 converges converge NOUN cana-1056 156 17 properties property NOUN cana-1056 156 18 for for ADP cana-1056 156 19 non non ADJ cana-1056 156 20 - - ADJ cana-1056 156 21 linear linear ADJ cana-1056 156 22 optimization optimization NOUN cana-1056 156 23 , , PUNCT cana-1056 156 24 ” " PUNCT cana-1056 156 25 2022 2022 NUM cana-1056 156 26 . . PUNCT cana-1056 157 1 [ [ X cana-1056 157 2 13 13 NUM cana-1056 157 3 ] ] X cana-1056 157 4 f. f. PROPN cana-1056 157 5 biglari biglari PROPN cana-1056 157 6 , , PUNCT cana-1056 157 7 m. m. NOUN cana-1056 157 8 a. a. PROPN cana-1056 157 9 hassan hassan PROPN cana-1056 157 10 , , PUNCT cana-1056 157 11 and and CCONJ cana-1056 157 12 w. w. PROPN cana-1056 157 13 j. j. PROPN cana-1056 157 14 leong leong PROPN cana-1056 157 15 , , PUNCT cana-1056 157 16 β€œ " PUNCT cana-1056 157 17 new new ADJ cana-1056 157 18 quasi quasi ADJ cana-1056 157 19 - - ADJ cana-1056 157 20 newton newton PROPN cana-1056 157 21 methods method NOUN cana-1056 157 22 via via ADP cana-1056 157 23 higher high ADJ cana-1056 157 24 order order NOUN cana-1056 157 25 tensor tensor NOUN cana-1056 157 26 models model NOUN cana-1056 157 27 , , PUNCT cana-1056 157 28 ” " PUNCT cana-1056 157 29 j. j. PROPN cana-1056 157 30 comput comput PROPN cana-1056 157 31 . . PUNCT cana-1056 158 1 appl appl PROPN cana-1056 158 2 . . PROPN cana-1056 158 3 math math PROPN cana-1056 158 4 . . PUNCT cana-1056 159 1 , , PUNCT cana-1056 159 2 vol vol NOUN cana-1056 159 3 . . PROPN cana-1056 159 4 235 235 NUM cana-1056 159 5 , , PUNCT cana-1056 159 6 no no INTJ cana-1056 159 7 . . NOUN cana-1056 159 8 8 8 NUM cana-1056 159 9 , , PUNCT cana-1056 159 10 pp pp ADJ cana-1056 159 11 . . PUNCT cana-1056 160 1 2412–2422 2412–2422 NUM cana-1056 160 2 , , PUNCT cana-1056 160 3 2011 2011 NUM cana-1056 160 4 . . PUNCT cana-1056 161 1 [ [ X cana-1056 161 2 14 14 NUM cana-1056 161 3 ] ] PUNCT cana-1056 161 4 z. z. PROPN cana-1056 161 5 wei wei PROPN cana-1056 161 6 , , PUNCT cana-1056 161 7 g. g. PROPN cana-1056 161 8 li li PROPN cana-1056 161 9 , , PUNCT cana-1056 161 10 and and CCONJ cana-1056 161 11 l. l. PROPN cana-1056 161 12 qi qi PROPN cana-1056 161 13 , , PUNCT cana-1056 161 14 β€œ " PUNCT cana-1056 161 15 new new ADJ cana-1056 161 16 quasi quasi NOUN cana-1056 161 17 - - ADJ cana-1056 161 18 newton newton PROPN cana-1056 161 19 methods method NOUN cana-1056 161 20 for for ADP cana-1056 161 21 unconstrained unconstrained ADJ cana-1056 161 22 optimization optimization NOUN cana-1056 161 23 problems problem NOUN cana-1056 161 24 , , PUNCT cana-1056 161 25 ” " PUNCT cana-1056 161 26 appl appl NOUN cana-1056 161 27 . . PROPN cana-1056 161 28 math math NOUN cana-1056 161 29 . . PUNCT cana-1056 162 1 comput comput NOUN cana-1056 162 2 . . PUNCT cana-1056 162 3 , , PUNCT cana-1056 162 4 vol vol NOUN cana-1056 162 5 . . PROPN cana-1056 163 1 175 175 NUM cana-1056 163 2 , , PUNCT cana-1056 163 3 no no INTJ cana-1056 163 4 . . NOUN cana-1056 163 5 2 2 NUM cana-1056 163 6 , , PUNCT cana-1056 163 7 pp pp ADJ cana-1056 163 8 . . PUNCT cana-1056 164 1 1156–1188 1156–1188 NUM cana-1056 164 2 , , PUNCT cana-1056 164 3 2006 2006 NUM cana-1056 164 4 . . PUNCT cana-1056 165 1 [ [ X cana-1056 165 2 15 15 NUM cana-1056 165 3 ] ] X cana-1056 165 4 p. p. NOUN cana-1056 165 5 li li PROPN cana-1056 165 6 , , PUNCT cana-1056 165 7 z. z. PROPN cana-1056 165 8 wang wang PROPN cana-1056 165 9 , , PUNCT cana-1056 165 10 d. d. PROPN cana-1056 165 11 luo luo PROPN cana-1056 165 12 , , PUNCT cana-1056 165 13 and and CCONJ cana-1056 165 14 h. h. PROPN cana-1056 165 15 pham pham PROPN cana-1056 165 16 , , PUNCT cana-1056 165 17 β€œ " PUNCT cana-1056 165 18 global global ADJ cana-1056 165 19 convergence convergence NOUN cana-1056 165 20 of of ADP cana-1056 165 21 a a DET cana-1056 165 22 modified modified ADJ cana-1056 165 23 two two NUM cana-1056 165 24 - - PUNCT cana-1056 165 25 parameter parameter NOUN cana-1056 165 26 scaled scale VERB cana-1056 165 27 bfgs bfgs ADJ cana-1056 165 28 method method NOUN cana-1056 165 29 with with ADP cana-1056 165 30 yuan yuan PROPN cana-1056 165 31 - - PUNCT cana-1056 165 32 wei wei PROPN cana-1056 165 33 - - PROPN cana-1056 165 34 lu lu PROPN cana-1056 165 35 line line NOUN cana-1056 165 36 search search NOUN cana-1056 165 37 for for ADP cana-1056 165 38 unconstrained unconstrained ADJ cana-1056 165 39 optimization optimization NOUN cana-1056 165 40 , , PUNCT cana-1056 165 41 ” " PUNCT cana-1056 165 42 math math NOUN cana-1056 165 43 . . PUNCT cana-1056 166 1 probl probl PROPN cana-1056 166 2 . . PUNCT cana-1056 167 1 eng eng PROPN cana-1056 167 2 . . PROPN cana-1056 167 3 , , PUNCT cana-1056 167 4 vol vol NOUN cana-1056 167 5 . . PUNCT cana-1056 167 6 2020 2020 NUM cana-1056 167 7 , , PUNCT cana-1056 167 8 pp pp ADV cana-1056 167 9 . . PUNCT cana-1056 168 1 1–15 1–15 NUM cana-1056 168 2 , , PUNCT cana-1056 168 3 2020 2020 NUM cana-1056 168 4 . . PUNCT cana-1056 169 1 [ [ X cana-1056 169 2 16 16 NUM cana-1056 169 3 ] ] X cana-1056 169 4 g. g. PROPN cana-1056 169 5 yuan yuan PROPN cana-1056 169 6 , , PUNCT cana-1056 169 7 z. z. PROPN cana-1056 169 8 wei wei PROPN cana-1056 169 9 , , PUNCT cana-1056 169 10 and and CCONJ cana-1056 169 11 x. x. NOUN cana-1056 169 12 lu lu PROPN cana-1056 169 13 , , PUNCT cana-1056 169 14 β€œ " PUNCT cana-1056 169 15 global global ADJ cana-1056 169 16 convergence convergence NOUN cana-1056 169 17 of of ADP cana-1056 169 18 bfgs bfgs ADJ cana-1056 169 19 and and CCONJ cana-1056 169 20 prp prp NOUN cana-1056 169 21 methods method NOUN cana-1056 169 22 under under ADP cana-1056 169 23 a a DET cana-1056 169 24 modified modify VERB cana-1056 169 25 weak weak ADJ cana-1056 169 26 wolfe wolfe PROPN cana-1056 169 27 – – PUNCT cana-1056 169 28 powell powell PROPN cana-1056 169 29 line line NOUN cana-1056 169 30 search search NOUN cana-1056 169 31 , , PUNCT cana-1056 169 32 ” " PUNCT cana-1056 169 33 appl appl NOUN cana-1056 169 34 . . PROPN cana-1056 169 35 math math PROPN cana-1056 169 36 . . PUNCT cana-1056 170 1 model model PROPN cana-1056 170 2 . . PUNCT cana-1056 171 1 , , PUNCT cana-1056 171 2 vol vol NOUN cana-1056 171 3 . . PROPN cana-1056 172 1 47 47 NUM cana-1056 172 2 , , PUNCT cana-1056 172 3 pp pp ADJ cana-1056 172 4 . . PUNCT cana-1056 173 1 811–825 811–825 NUM cana-1056 173 2 , , PUNCT cana-1056 173 3 2017 2017 NUM cana-1056 173 4 . . PUNCT cana-1056 174 1 [ [ X cana-1056 174 2 17 17 NUM cana-1056 174 3 ] ] X cana-1056 174 4 g. g. PROPN cana-1056 174 5 yuan yuan PROPN cana-1056 174 6 , , PUNCT cana-1056 174 7 z. z. PROPN cana-1056 174 8 sheng sheng PROPN cana-1056 174 9 , , PUNCT cana-1056 174 10 b. b. PROPN cana-1056 174 11 wang wang PROPN cana-1056 174 12 , , PUNCT cana-1056 174 13 w. w. PROPN cana-1056 174 14 hu hu PROPN cana-1056 174 15 , , PUNCT cana-1056 174 16 and and CCONJ cana-1056 174 17 c. c. PROPN cana-1056 174 18 li li PROPN cana-1056 174 19 , , PUNCT cana-1056 174 20 β€œ " PUNCT cana-1056 174 21 the the DET cana-1056 174 22 global global ADJ cana-1056 174 23 convergence convergence NOUN cana-1056 174 24 of of ADP cana-1056 174 25 a a DET cana-1056 174 26 modified modify VERB cana-1056 174 27 bfgs bfgs ADJ cana-1056 174 28 method method NOUN cana-1056 174 29 for for ADP cana-1056 174 30 nonconvex nonconvex NOUN cana-1056 174 31 functions function NOUN cana-1056 174 32 , , PUNCT cana-1056 174 33 ” " PUNCT cana-1056 174 34 j. j. PROPN cana-1056 174 35 comput comput PROPN cana-1056 174 36 . . PUNCT cana-1056 175 1 appl appl PROPN cana-1056 175 2 . . PROPN cana-1056 175 3 math math PROPN cana-1056 175 4 . . PUNCT cana-1056 176 1 , , PUNCT cana-1056 176 2 vol vol NOUN cana-1056 176 3 . . PROPN cana-1056 176 4 327 327 NUM cana-1056 176 5 , , PUNCT cana-1056 176 6 pp pp ADJ cana-1056 176 7 . . PUNCT cana-1056 177 1 274–294 274–294 NUM cana-1056 177 2 , , PUNCT cana-1056 177 3 2018 2018 NUM cana-1056 177 4 . . PUNCT cana-1056 178 1 [ [ X cana-1056 178 2 18 18 NUM cana-1056 178 3 ] ] PUNCT cana-1056 178 4 a. a. PROPN cana-1056 178 5 y. y. PROPN cana-1056 178 6 al al PROPN cana-1056 178 7 - - PUNCT cana-1056 178 8 bayati bayati PROPN cana-1056 178 9 and and CCONJ cana-1056 178 10 m. m. NOUN cana-1056 178 11 m. m. PROPN cana-1056 178 12 m. m. PROPN cana-1056 178 13 ali ali PROPN cana-1056 178 14 , , PUNCT cana-1056 178 15 β€œ " PUNCT cana-1056 178 16 new new ADJ cana-1056 178 17 multi multi ADJ cana-1056 178 18 - - ADJ cana-1056 178 19 step step ADJ cana-1056 178 20 three three NUM cana-1056 178 21 - - PUNCT cana-1056 178 22 term term NOUN cana-1056 178 23 conjugate conjugate ADJ cana-1056 178 24 gradient gradient NOUN cana-1056 178 25 algorithms algorithm NOUN cana-1056 178 26 with with ADP cana-1056 178 27 inexact inexact ADJ cana-1056 178 28 line line NOUN cana-1056 178 29 searches search NOUN cana-1056 178 30 , , PUNCT cana-1056 178 31 ” " PUNCT cana-1056 178 32 indones indone NOUN cana-1056 178 33 . . PUNCT cana-1056 179 1 j. j. PROPN cana-1056 179 2 electr electr PROPN cana-1056 179 3 . . PUNCT cana-1056 180 1 eng eng PROPN cana-1056 180 2 . . PUNCT cana-1056 181 1 comput comput PROPN cana-1056 181 2 . . PUNCT cana-1056 182 1 sci sci PROPN cana-1056 182 2 . . PROPN cana-1056 182 3 , , PUNCT cana-1056 182 4 vol vol NOUN cana-1056 182 5 . . PROPN cana-1056 182 6 19 19 NUM cana-1056 182 7 , , PUNCT cana-1056 182 8 no no INTJ cana-1056 182 9 . . NOUN cana-1056 182 10 3 3 NUM cana-1056 182 11 , , PUNCT cana-1056 182 12 pp pp ADJ cana-1056 182 13 . . PUNCT cana-1056 182 14 1564–1573 1564–1573 NUM cana-1056 182 15 , , PUNCT cana-1056 182 16 2020 2020 NUM cana-1056 182 17 .. .. PUNCT cana-1056 183 1 [ [ X cana-1056 183 2 19 19 NUM cana-1056 183 3 ] ] PUNCT cana-1056 183 4 b. b. PROPN cana-1056 183 5 a. a. PROPN cana-1056 183 6 hassan hassan PROPN cana-1056 183 7 and and CCONJ cana-1056 183 8 m. m. PROPN cana-1056 183 9 s. s. PROPN cana-1056 183 10 ranen ranen PROPN cana-1056 183 11 , , PUNCT cana-1056 183 12 β€œ " PUNCT cana-1056 183 13 a a DET cana-1056 183 14 new new ADJ cana-1056 183 15 type type NOUN cana-1056 183 16 of of ADP cana-1056 183 17 self self NOUN cana-1056 183 18 - - PUNCT cana-1056 183 19 scaling scale VERB cana-1056 183 20 quasi quasi NOUN cana-1056 183 21 - - NOUN cana-1056 183 22 newton newton PROPN cana-1056 183 23 for for ADP cana-1056 183 24 unconstrained unconstrained ADJ cana-1056 183 25 optimization optimization NOUN cana-1056 183 26 , , PUNCT cana-1056 183 27 ” " PUNCT cana-1056 183 28 int int NOUN cana-1056 183 29 . . PUNCT cana-1056 184 1 j. j. PROPN cana-1056 184 2 adv adv PROPN cana-1056 184 3 . . PUNCT cana-1056 185 1 scince scince NOUN cana-1056 185 2 technol technol NOUN cana-1056 185 3 . . PROPN cana-1056 185 4 , , PUNCT cana-1056 185 5 vol vol NOUN cana-1056 185 6 . . PROPN cana-1056 185 7 29 29 NUM cana-1056 185 8 , , PUNCT cana-1056 185 9 no no INTJ cana-1056 185 10 . . NOUN cana-1056 185 11 4 4 NUM cana-1056 185 12 , , PUNCT cana-1056 185 13 pp pp ADJ cana-1056 185 14 . . PUNCT cana-1056 185 15 10822–10827 10822–10827 NUM cana-1056 185 16 , , PUNCT cana-1056 185 17 2020 2020 NUM cana-1056 185 18 . . PUNCT cana-1056 186 1 [ [ X cana-1056 186 2 20 20 NUM cana-1056 186 3 ] ] X cana-1056 186 4 n. n. PROPN cana-1056 186 5 i. i. PROPN cana-1056 186 6 m. m. PROPN cana-1056 186 7 gould gould PROPN cana-1056 186 8 , , PUNCT cana-1056 186 9 d. d. PROPN cana-1056 186 10 orban orban PROPN cana-1056 186 11 , , PUNCT cana-1056 186 12 and and CCONJ cana-1056 186 13 p. p. PROPN cana-1056 186 14 l. l. PROPN cana-1056 186 15 toint toint PROPN cana-1056 186 16 , , PUNCT cana-1056 186 17 β€œ " PUNCT cana-1056 186 18 cutest cut ADJ cana-1056 186 19 : : PUNCT cana-1056 186 20 a a DET cana-1056 186 21 constrained constrain VERB cana-1056 186 22 and and CCONJ cana-1056 186 23 unconstrained unconstrained ADJ cana-1056 186 24 testing testing NOUN cana-1056 186 25 environment environment NOUN cana-1056 186 26 with with ADP cana-1056 186 27 safe safe ADJ cana-1056 186 28 threads thread NOUN cana-1056 186 29 for for ADP cana-1056 186 30 mathematical mathematical ADJ cana-1056 186 31 optimization optimization NOUN cana-1056 186 32 , , PUNCT cana-1056 186 33 ” " PUNCT cana-1056 186 34 comput comput NOUN cana-1056 186 35 . . PUNCT cana-1056 187 1 optim optim PROPN cana-1056 187 2 . . PUNCT cana-1056 188 1 appl appl PROPN cana-1056 188 2 . . PROPN cana-1056 188 3 , , PUNCT cana-1056 188 4 vol vol NOUN cana-1056 188 5 . . PROPN cana-1056 188 6 60 60 NUM cana-1056 188 7 , , PUNCT cana-1056 188 8 pp pp ADJ cana-1056 188 9 . . PUNCT cana-1056 189 1 545–557 545–557 NUM cana-1056 189 2 , , PUNCT cana-1056 189 3 2015 2015 NUM cana-1056 189 4 . . PUNCT cana-1056 190 1 communications communication NOUN cana-1056 190 2 on on ADP cana-1056 190 3 applied apply VERB cana-1056 190 4 nonlinear nonlinear ADJ cana-1056 190 5 analysis analysis NOUN cana-1056 190 6 issn issn NOUN cana-1056 190 7 : : PUNCT cana-1056 190 8 1074 1074 NUM cana-1056 190 9 - - PUNCT cana-1056 190 10 133x 133x NUM cana-1056 190 11 vol vol NOUN cana-1056 190 12 31 31 NUM cana-1056 190 13 no no NOUN cana-1056 190 14 . . PUNCT cana-1056 191 1 5s 5s NUM cana-1056 191 2 ( ( PUNCT cana-1056 191 3 2024 2024 NUM cana-1056 191 4 ) ) PUNCT cana-1056 191 5 381 381 NUM cana-1056 191 6 https://internationalpubls.com https://internationalpubls.com X cana-1056 191 7 appendix appendix VERB cana-1056 191 8 the the DET cana-1056 191 9 test test NOUN cana-1056 191 10 function function NOUN cana-1056 191 11 for for ADP cana-1056 191 12 unconstrained unconstrained ADJ cana-1056 191 13 optimization optimization NOUN cana-1056 191 14 no no INTJ cana-1056 191 15 . . PUNCT cana-1056 192 1 the the DET cana-1056 192 2 test test NOUN cana-1056 192 3 function function NOUN cana-1056 192 4 1 1 NUM cana-1056 192 5 beale beale NOUN cana-1056 192 6 2 2 NUM cana-1056 192 7 trigonametric trigonametric NOUN cana-1056 192 8 3 3 NUM cana-1056 192 9 generalized generalized ADJ cana-1056 192 10 quadratic quadratic ADJ cana-1056 192 11 4 4 NUM cana-1056 192 12 hager hager NOUN cana-1056 192 13 5 5 NUM cana-1056 192 14 diagonal diagonal ADJ cana-1056 192 15 1 1 NUM cana-1056 192 16 6 6 NUM cana-1056 192 17 diagonal diagonal ADJ cana-1056 192 18 2 2 NUM cana-1056 192 19 7 7 NUM cana-1056 192 20 edensch edensch NUM cana-1056 192 21 8 8 NUM cana-1056 192 22 edenschnb edenschnb NOUN cana-1056 192 23 9 9 NUM cana-1056 192 24 fletcher fletcher NOUN cana-1056 192 25 10 10 NUM cana-1056 192 26 nondia nondia PROPN cana-1056 192 27 11 11 NUM cana-1056 192 28 extend extend NOUN cana-1056 192 29 rosenbrock rosenbrock NOUN cana-1056 192 30 12 12 NUM cana-1056 192 31 extend extend NOUN cana-1056 192 32 powell powell PROPN cana-1056 192 33 13 13 NUM cana-1056 192 34 extend extend NOUN cana-1056 192 35 hiebert hiebert NOUN cana-1056 192 36 14 14 NUM cana-1056 192 37 extend extend NOUN cana-1056 192 38 wood wood NOUN cana-1056 192 39 15 15 NUM cana-1056 192 40 extend extend NOUN cana-1056 192 41 quadratic quadratic ADJ