Theoretical analysis, numerical verification and geometrical representation of new three-step DTZD algorithm for time-varying nonlinear equations solving
To solve time-varying nonlinear equations, Zhang et al. have developed a one-step discrete-time Zhang dynamics (DTZD) algorithm with O(τ2) error pattern, where τ denotes the sampling gap. In this paper, by exploiting the Taylor-type difference rule, a new three-step DTZD algorithm with O(τ3) error p...
Uložené v:
| Vydané v: | Neurocomputing (Amsterdam) Ročník 214; s. 516 - 526 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
19.11.2016
|
| Predmet: | |
| ISSN: | 0925-2312, 1872-8286 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | To solve time-varying nonlinear equations, Zhang et al. have developed a one-step discrete-time Zhang dynamics (DTZD) algorithm with O(τ2) error pattern, where τ denotes the sampling gap. In this paper, by exploiting the Taylor-type difference rule, a new three-step DTZD algorithm with O(τ3) error pattern is proposed and investigated for time-varying nonlinear equations solving. Note that such an algorithm can achieve better computational performance than the one-step DTZD algorithm. As for the proposed three-step DTZD algorithm, theoretical results are given to show its excellent computational property. Comparative numerical results further substantiate the efficacy and superiority of the proposed three-step DTZD algorithm for solving time-varying nonlinear equations, as compared with the one-step DTZD algorithm. Besides, the geometric representation of the proposed three-step DTZD algorithm is provided for time-varying nonlinear equations solving. |
|---|---|
| AbstractList | To solve time-varying nonlinear equations, Zhang et al. have developed a one-step discrete-time Zhang dynamics (DTZD) algorithm with O(τ2) error pattern, where τ denotes the sampling gap. In this paper, by exploiting the Taylor-type difference rule, a new three-step DTZD algorithm with O(τ3) error pattern is proposed and investigated for time-varying nonlinear equations solving. Note that such an algorithm can achieve better computational performance than the one-step DTZD algorithm. As for the proposed three-step DTZD algorithm, theoretical results are given to show its excellent computational property. Comparative numerical results further substantiate the efficacy and superiority of the proposed three-step DTZD algorithm for solving time-varying nonlinear equations, as compared with the one-step DTZD algorithm. Besides, the geometric representation of the proposed three-step DTZD algorithm is provided for time-varying nonlinear equations solving. |
| Author | Nie, Zhuoyun Yan, Laicheng Guo, Dongsheng |
| Author_xml | – sequence: 1 givenname: Dongsheng surname: Guo fullname: Guo, Dongsheng email: gdongsh@hqu.edu.cn – sequence: 2 givenname: Zhuoyun surname: Nie fullname: Nie, Zhuoyun – sequence: 3 givenname: Laicheng surname: Yan fullname: Yan, Laicheng |
| BookMark | eNqFUMtOIzEQtFZBIoH9Aw7-ACbY7ZnJhAMSgl1AQuISLnuxPJ524mjGDrYTxKfwt2uYPXFgpZb6UV0lVc3IxHmHhJxxNueM1xfbucO99sMc8jZnuQT8IFPeLKBooKknZMqWUBUgOByTWYxbxviCw3JK3lcb9AGT1aqnyqn-Ldp4Tt1-wPB5O-Ru8pSsd_mho2v0A6YRDLgLGNGlEfaGOnylaRMQi5hwR29Xf26p6tc-2LQZqPGBJjtgcVDhzbo1zUZ661AFii_7T5FIo-8PGTslR0b1EX_-6yfk-fev1c198fh093Bz_VhowepUQFd2AMBKqAw0FTelWLYL3mDZiqoTogZtlo0wdduW0IHCGirFNJblgldtVYkTcjnq6uBjDGiktqOfFJTtJWfyI2S5lWPI8iNkyXIJyOTyC3kX7JDN_Y92NdIwGztYDDJqi05jZwPqJDtvvxf4C4k7n2k |
| CitedBy_id | crossref_primary_10_1016_j_neucom_2020_05_093 crossref_primary_10_1109_TII_2017_2780892 crossref_primary_10_1016_j_neucom_2019_04_054 crossref_primary_10_1007_s11075_018_0564_5 crossref_primary_10_1016_j_neucom_2017_05_017 crossref_primary_10_1007_s11071_017_3432_2 crossref_primary_10_1155_2021_6627298 crossref_primary_10_1016_j_neucom_2023_126937 crossref_primary_10_1007_s11063_019_10107_8 crossref_primary_10_1016_j_neucom_2018_01_033 crossref_primary_10_1016_j_neucom_2018_11_064 crossref_primary_10_1109_TNNLS_2020_3041364 crossref_primary_10_1109_TSMC_2017_2656941 crossref_primary_10_1016_j_apm_2019_08_001 crossref_primary_10_1016_j_neucom_2017_09_032 crossref_primary_10_1016_j_jfranklin_2022_05_014 crossref_primary_10_1109_ACCESS_2020_3035530 crossref_primary_10_1109_TCYB_2018_2818747 crossref_primary_10_1007_s11075_017_0302_4 crossref_primary_10_1016_j_neucom_2018_02_059 crossref_primary_10_1109_TNNLS_2017_2761443 crossref_primary_10_1016_j_neucom_2018_10_031 crossref_primary_10_1109_TCYB_2021_3051035 crossref_primary_10_1016_j_neucom_2022_03_010 crossref_primary_10_1109_TII_2018_2789438 crossref_primary_10_1109_TSMC_2017_2693400 crossref_primary_10_1109_ACCESS_2019_2937686 crossref_primary_10_3390_s19010074 crossref_primary_10_1109_TII_2018_2861908 crossref_primary_10_1016_j_neucom_2018_03_053 crossref_primary_10_1016_j_neucom_2020_07_115 crossref_primary_10_1007_s11075_020_01061_x crossref_primary_10_1007_s11075_018_0581_4 crossref_primary_10_1016_j_neucom_2020_02_011 crossref_primary_10_1016_j_neucom_2019_11_031 crossref_primary_10_1016_j_neucom_2019_11_036 crossref_primary_10_1109_TSMC_2018_2856266 crossref_primary_10_1016_j_laa_2019_06_028 crossref_primary_10_1002_asjc_2315 crossref_primary_10_1109_TFUZZ_2021_3115969 crossref_primary_10_1016_j_neucom_2020_11_012 crossref_primary_10_1109_TNNLS_2019_2938866 |
| Cites_doi | 10.1109/TNNLS.2013.2280905 10.1016/j.neucom.2016.01.020 10.1016/j.neucom.2015.09.043 10.1007/s11075-012-9690-7 10.1016/j.neucom.2014.09.047 10.1109/TC.2002.1146704 10.1016/j.neucom.2015.08.031 10.1109/TNNLS.2015.2496658 10.1016/j.neucom.2016.02.017 10.1109/12.863031 10.1007/s00521-010-0452-y 10.1109/ICAL.2009.5262860 10.1007/s100920300006 10.1109/TNNLS.2012.2223484 10.1016/j.cam.2014.05.027 10.1007/978-3-642-21105-8_46 10.1016/j.neucom.2015.04.032 10.1016/j.neucom.2015.11.069 10.1016/j.ipl.2005.11.015 10.1007/s00211-006-0025-2 10.1016/j.neucom.2015.04.070 10.1016/j.neucom.2005.11.006 |
| ContentType | Journal Article |
| Copyright | 2016 Elsevier B.V. |
| Copyright_xml | – notice: 2016 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.neucom.2016.06.032 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1872-8286 |
| EndPage | 526 |
| ExternalDocumentID | 10_1016_j_neucom_2016_06_032 S0925231216306701 |
| GroupedDBID | --- --K --M .DC .~1 0R~ 123 1B1 1~. 1~5 4.4 457 4G. 53G 5VS 7-5 71M 8P~ 9JM 9JN AABNK AACTN AADPK AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXLA AAXUO AAYFN ABBOA ABCQJ ABFNM ABJNI ABMAC ABYKQ ACDAQ ACGFS ACRLP ACZNC ADBBV ADEZE AEBSH AEKER AENEX AFKWA AFTJW AFXIZ AGHFR AGUBO AGWIK AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD AXJTR BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ IHE J1W KOM LG9 M41 MO0 MOBAO N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 RIG ROL RPZ SDF SDG SDP SES SPC SPCBC SSN SSV SSZ T5K ZMT ~G- 29N 9DU AAQXK AATTM AAXKI AAYWO AAYXX ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADJOM ADMUD ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS FEDTE FGOYB HLZ HVGLF HZ~ R2- SBC SEW WUQ XPP ~HD |
| ID | FETCH-LOGICAL-c306t-2d4d2220425f2851f439b718e4b35d3362cf983f6bb42d2ae625a0ce44715b553 |
| ISICitedReferencesCount | 58 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000386741300049&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0925-2312 |
| IngestDate | Sat Nov 29 07:18:37 EST 2025 Tue Nov 18 22:18:34 EST 2025 Fri Feb 23 02:30:25 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Time-varying nonlinear equations Theoretical analysis Discrete-time Zhang dynamics Three-step algorithm Geometric representation |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c306t-2d4d2220425f2851f439b718e4b35d3362cf983f6bb42d2ae625a0ce44715b553 |
| PageCount | 11 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_neucom_2016_06_032 crossref_primary_10_1016_j_neucom_2016_06_032 elsevier_sciencedirect_doi_10_1016_j_neucom_2016_06_032 |
| PublicationCentury | 2000 |
| PublicationDate | 2016-11-19 |
| PublicationDateYYYYMMDD | 2016-11-19 |
| PublicationDate_xml | – month: 11 year: 2016 text: 2016-11-19 day: 19 |
| PublicationDecade | 2010 |
| PublicationTitle | Neurocomputing (Amsterdam) |
| PublicationYear | 2016 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Xiao (bib15) 2015; 167 Y. Zhang, P. Xu, N. Tan, Further studies on Zhang neural-dynamics and gradient dynamics for online nonlinear equations solving, in: Proceedings of IEEE International Conference on Automation and Logistics, 2009, pp. 566–571. Zhang, Guo (bib23) 2015 Kong, Cai, Yu, Li (bib3) 2006; 98 Shu, Liu, Liu (bib27) 2016; 173 Xiao (bib22) 2016; 173 Frontini (bib4) 2003; 40 He, Li, Huang, Li, Huang (bib12) 2014; 25 Xiao, Lu (bib21) 2015; 151 Zhang, Yi, Guo, Zheng (bib19) 2011; 20 Mead (bib30) 1989 S.K. Mitra, Digital Signal Processing—A Computer-Based Approach, third ed., Tsinghua University Press, Beijing, 2006. Li, Yu, Huang, Chen, He (bib13) 2016; 27 Pineiro, Bruguera (bib2) 2002; 51 Ujevic (bib6) 2006; 174 Sharma (bib11) 2016; 273 Zhang, Jin, Guo, Yin, Chou (bib29) 2015; 273 Xu, Li, He, Huang (bib14) 2016; 190 Griffiths, Higham (bib33) 2010 Sharma (bib5) 2005; 169 Jarina Banu, Balasubramaniam (bib26) 2016; 179 J.H. Mathews, K.D. Fink, Numerical Methods Using MATLAB, fourth ed., Prentice Hall, New Jersey, 2004. Zhang, Li, Guo, Ke, Chen, Discrete-time (bib9) 2013; 64 Yang (bib8) 2013; 219 Zhang, Yi (bib20) 2011 Zhang, Ke, Li, Guo (bib18) 2011; 6675 Ercegovac, Lang, Muller, Tisserand (bib1) 2000; 49 Perez-IIzarbe (bib28) 2013; 24 Bao, Zeng (bib25) 2016; 193 Neta, Chun, Scott (bib10) 2014; 227 Guo, Zhang, Xiao, Mao, Liu (bib24) 2015; 167 Chun (bib7) 2006; 104 Zhang (bib16) 2006; 70 Ercegovac (10.1016/j.neucom.2016.06.032_bib1) 2000; 49 Bao (10.1016/j.neucom.2016.06.032_bib25) 2016; 193 Pineiro (10.1016/j.neucom.2016.06.032_bib2) 2002; 51 Zhang (10.1016/j.neucom.2016.06.032_bib20) 2011 Jarina Banu (10.1016/j.neucom.2016.06.032_bib26) 2016; 179 Zhang (10.1016/j.neucom.2016.06.032_bib19) 2011; 20 Guo (10.1016/j.neucom.2016.06.032_bib24) 2015; 167 Neta (10.1016/j.neucom.2016.06.032_bib10) 2014; 227 Mead (10.1016/j.neucom.2016.06.032_bib30) 1989 Kong (10.1016/j.neucom.2016.06.032_bib3) 2006; 98 He (10.1016/j.neucom.2016.06.032_bib12) 2014; 25 Chun (10.1016/j.neucom.2016.06.032_bib7) 2006; 104 Xiao (10.1016/j.neucom.2016.06.032_bib15) 2015; 167 Xu (10.1016/j.neucom.2016.06.032_bib14) 2016; 190 Griffiths (10.1016/j.neucom.2016.06.032_bib33) 2010 Ujevic (10.1016/j.neucom.2016.06.032_bib6) 2006; 174 Zhang (10.1016/j.neucom.2016.06.032_bib23) 2015 Xiao (10.1016/j.neucom.2016.06.032_bib22) 2016; 173 Sharma (10.1016/j.neucom.2016.06.032_bib11) 2016; 273 Shu (10.1016/j.neucom.2016.06.032_bib27) 2016; 173 Li (10.1016/j.neucom.2016.06.032_bib13) 2016; 27 Frontini (10.1016/j.neucom.2016.06.032_bib4) 2003; 40 Zhang (10.1016/j.neucom.2016.06.032_bib29) 2015; 273 Yang (10.1016/j.neucom.2016.06.032_bib8) 2013; 219 Zhang (10.1016/j.neucom.2016.06.032_bib9) 2013; 64 10.1016/j.neucom.2016.06.032_bib31 10.1016/j.neucom.2016.06.032_bib32 Sharma (10.1016/j.neucom.2016.06.032_bib5) 2005; 169 Zhang (10.1016/j.neucom.2016.06.032_bib18) 2011; 6675 Perez-IIzarbe (10.1016/j.neucom.2016.06.032_bib28) 2013; 24 Xiao (10.1016/j.neucom.2016.06.032_bib21) 2015; 151 10.1016/j.neucom.2016.06.032_bib17 Zhang (10.1016/j.neucom.2016.06.032_bib16) 2006; 70 |
| References_xml | – volume: 273 start-page: 29 year: 2015 end-page: 40 ident: bib29 article-title: Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization publication-title: J. Comput. Appl. Math. – volume: 6675 start-page: 393 year: 2011 end-page: 402 ident: bib18 article-title: Comparison on continuous-time Zhang dynamics and Newton–Raphson iteration for online solution of nonlinear equations publication-title: Lect. Notes Comput. Sci. – year: 2011 ident: bib20 article-title: Zhang Neural Networks and Neural-Dynamic Method – volume: 70 start-page: 513 year: 2006 end-page: 524 ident: bib16 article-title: A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network publication-title: Neurocomputing – volume: 273 start-page: 793 year: 2016 end-page: 796 ident: bib11 article-title: A note on the convergence order of some recent methods for solving nonlinear equations publication-title: Appl. Math. Comput. – volume: 173 start-page: 1983 year: 2016 end-page: 1988 ident: bib22 article-title: A nonlinearly activated neural dynamics and its finite-time solution to time-varying nonlinear equation publication-title: Neurocomputing – reference: J.H. Mathews, K.D. Fink, Numerical Methods Using MATLAB, fourth ed., Prentice Hall, New Jersey, 2004. – volume: 169 start-page: 242 year: 2005 end-page: 246 ident: bib5 article-title: A composite third order Newton–Steffensen method for solving nonlinear equations publication-title: Appl. Math. Comput. – volume: 27 start-page: 308 year: 2016 end-page: 321 ident: bib13 article-title: A generalized Hopfield network for nonsmooth constrained convex optimization publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 193 start-page: 242 year: 2016 end-page: 249 ident: bib25 article-title: Global asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functions publication-title: Neurocomputing – volume: 151 start-page: 246 year: 2015 end-page: 251 ident: bib21 article-title: Finite-time solution to nonlinear equation using recurrent neural dynamics with a specially-constructed activation function publication-title: Neurocomputing – volume: 104 start-page: 297 year: 2006 end-page: 315 ident: bib7 article-title: Construction of Newton-like iteration methods for solving nonlinear equations publication-title: Numer. Math. – volume: 179 start-page: 126 year: 2016 end-page: 134 ident: bib26 article-title: Robust stability analysis for discrete-time neural networks with time-varying leakage delays and random parameter uncertainties publication-title: Neurocomputing – volume: 174 start-page: 1416 year: 2006 end-page: 1426 ident: bib6 article-title: A method for solving nonlinear equations publication-title: Appl. Math. Comput. – volume: 167 start-page: 254 year: 2015 end-page: 259 ident: bib15 article-title: A finite-time convergent neural dynamics for online solution of time-varying linear complex matrix equation publication-title: Neurocomputing – volume: 49 start-page: 628 year: 2000 end-page: 637 ident: bib1 article-title: A, reciprocation, square root, inverse square root, and some elementary functions using small multipliers publication-title: IEEE Trans. Comput. – reference: S.K. Mitra, Digital Signal Processing—A Computer-Based Approach, third ed., Tsinghua University Press, Beijing, 2006. – volume: 190 start-page: 172 year: 2016 end-page: 178 ident: bib14 article-title: Recurrent neural network for solving model predictive control problem in application of four-tank benchmark publication-title: Neurocomputing – year: 2015 ident: bib23 article-title: Zhang Functions and Various Models – year: 1989 ident: bib30 article-title: Analog VLSI and Neural Systems – volume: 40 start-page: 109 year: 2003 end-page: 119 ident: bib4 article-title: Hermite interpolation and a new iterative method for the computation of the roots of non-linear equations publication-title: Calcolo – volume: 167 start-page: 578 year: 2015 end-page: 586 ident: bib24 article-title: Common nature of learning between BP-type and Hopfield-type neural networks publication-title: Neurocomputing – year: 2010 ident: bib33 article-title: Numerical Methods for Ordinary Differential Equations: Initial Value Problems – volume: 25 start-page: 824 year: 2014 end-page: 830 ident: bib12 article-title: A recurrent neural network for solving bilevel linear programming problem publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 173 start-page: 1706 year: 2016 end-page: 1714 ident: bib27 article-title: Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay publication-title: Neurocomputing – reference: Y. Zhang, P. Xu, N. Tan, Further studies on Zhang neural-dynamics and gradient dynamics for online nonlinear equations solving, in: Proceedings of IEEE International Conference on Automation and Logistics, 2009, pp. 566–571. – volume: 98 start-page: 1 year: 2006 end-page: 5 ident: bib3 article-title: Improved generalized Atkin algorithm for computing square roots in finite fields publication-title: Inf. Process. Lett. – volume: 51 start-page: 1377 year: 2002 end-page: 1388 ident: bib2 article-title: High-speed double-precision computation of reciprocal, division, square root, and inverse square root publication-title: IEEE Trans. Comput. – volume: 64 start-page: 721 year: 2013 end-page: 740 ident: bib9 article-title: GD and NI for solving nonlinear time-varying equations publication-title: Numer. Algorithms – volume: 24 start-page: 322 year: 2013 end-page: 328 ident: bib28 article-title: New discrete-time recurrent neural network proposal for quadratic optimization with general linear constraints publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 20 start-page: 1 year: 2011 end-page: 7 ident: bib19 article-title: Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation publication-title: Neural Comput. Appl. – volume: 219 start-page: 10682 year: 2013 end-page: 10694 ident: bib8 article-title: A higher-order Levenberg–Marquardt method for nonlinear equations publication-title: Appl. Math. Comput. – volume: 227 start-page: 567 year: 2014 end-page: 592 ident: bib10 article-title: Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations publication-title: Appl. Math. Comput. – volume: 169 start-page: 242 year: 2005 ident: 10.1016/j.neucom.2016.06.032_bib5 article-title: A composite third order Newton–Steffensen method for solving nonlinear equations publication-title: Appl. Math. Comput. – volume: 25 start-page: 824 issue: 4 year: 2014 ident: 10.1016/j.neucom.2016.06.032_bib12 article-title: A recurrent neural network for solving bilevel linear programming problem publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2013.2280905 – volume: 190 start-page: 172 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib14 article-title: Recurrent neural network for solving model predictive control problem in application of four-tank benchmark publication-title: Neurocomputing doi: 10.1016/j.neucom.2016.01.020 – volume: 173 start-page: 1706 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib27 article-title: Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay publication-title: Neurocomputing doi: 10.1016/j.neucom.2015.09.043 – volume: 64 start-page: 721 issue: 4 year: 2013 ident: 10.1016/j.neucom.2016.06.032_bib9 article-title: GD and NI for solving nonlinear time-varying equations publication-title: Numer. Algorithms doi: 10.1007/s11075-012-9690-7 – volume: 151 start-page: 246 year: 2015 ident: 10.1016/j.neucom.2016.06.032_bib21 article-title: Finite-time solution to nonlinear equation using recurrent neural dynamics with a specially-constructed activation function publication-title: Neurocomputing doi: 10.1016/j.neucom.2014.09.047 – volume: 273 start-page: 793 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib11 article-title: A note on the convergence order of some recent methods for solving nonlinear equations publication-title: Appl. Math. Comput. – volume: 51 start-page: 1377 issue: 12 year: 2002 ident: 10.1016/j.neucom.2016.06.032_bib2 article-title: High-speed double-precision computation of reciprocal, division, square root, and inverse square root publication-title: IEEE Trans. Comput. doi: 10.1109/TC.2002.1146704 – volume: 173 start-page: 1983 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib22 article-title: A nonlinearly activated neural dynamics and its finite-time solution to time-varying nonlinear equation publication-title: Neurocomputing doi: 10.1016/j.neucom.2015.08.031 – ident: 10.1016/j.neucom.2016.06.032_bib32 – volume: 27 start-page: 308 issue: 2 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib13 article-title: A generalized Hopfield network for nonsmooth constrained convex optimization publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2496658 – volume: 193 start-page: 242 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib25 article-title: Global asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functions publication-title: Neurocomputing doi: 10.1016/j.neucom.2016.02.017 – year: 2011 ident: 10.1016/j.neucom.2016.06.032_bib20 – volume: 49 start-page: 628 issue: 7 year: 2000 ident: 10.1016/j.neucom.2016.06.032_bib1 article-title: A, reciprocation, square root, inverse square root, and some elementary functions using small multipliers publication-title: IEEE Trans. Comput. doi: 10.1109/12.863031 – volume: 20 start-page: 1 issue: 1 year: 2011 ident: 10.1016/j.neucom.2016.06.032_bib19 article-title: Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation publication-title: Neural Comput. Appl. doi: 10.1007/s00521-010-0452-y – ident: 10.1016/j.neucom.2016.06.032_bib17 doi: 10.1109/ICAL.2009.5262860 – year: 2010 ident: 10.1016/j.neucom.2016.06.032_bib33 – volume: 40 start-page: 109 year: 2003 ident: 10.1016/j.neucom.2016.06.032_bib4 article-title: Hermite interpolation and a new iterative method for the computation of the roots of non-linear equations publication-title: Calcolo doi: 10.1007/s100920300006 – volume: 227 start-page: 567 year: 2014 ident: 10.1016/j.neucom.2016.06.032_bib10 article-title: Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations publication-title: Appl. Math. Comput. – volume: 219 start-page: 10682 year: 2013 ident: 10.1016/j.neucom.2016.06.032_bib8 article-title: A higher-order Levenberg–Marquardt method for nonlinear equations publication-title: Appl. Math. Comput. – volume: 24 start-page: 322 issue: 2 year: 2013 ident: 10.1016/j.neucom.2016.06.032_bib28 article-title: New discrete-time recurrent neural network proposal for quadratic optimization with general linear constraints publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2012.2223484 – year: 1989 ident: 10.1016/j.neucom.2016.06.032_bib30 – volume: 174 start-page: 1416 year: 2006 ident: 10.1016/j.neucom.2016.06.032_bib6 article-title: A method for solving nonlinear equations publication-title: Appl. Math. Comput. – volume: 273 start-page: 29 year: 2015 ident: 10.1016/j.neucom.2016.06.032_bib29 article-title: Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2014.05.027 – volume: 6675 start-page: 393 year: 2011 ident: 10.1016/j.neucom.2016.06.032_bib18 article-title: Comparison on continuous-time Zhang dynamics and Newton–Raphson iteration for online solution of nonlinear equations publication-title: Lect. Notes Comput. Sci. doi: 10.1007/978-3-642-21105-8_46 – volume: 167 start-page: 578 year: 2015 ident: 10.1016/j.neucom.2016.06.032_bib24 article-title: Common nature of learning between BP-type and Hopfield-type neural networks publication-title: Neurocomputing doi: 10.1016/j.neucom.2015.04.032 – year: 2015 ident: 10.1016/j.neucom.2016.06.032_bib23 – ident: 10.1016/j.neucom.2016.06.032_bib31 – volume: 179 start-page: 126 year: 2016 ident: 10.1016/j.neucom.2016.06.032_bib26 article-title: Robust stability analysis for discrete-time neural networks with time-varying leakage delays and random parameter uncertainties publication-title: Neurocomputing doi: 10.1016/j.neucom.2015.11.069 – volume: 98 start-page: 1 issue: 1 year: 2006 ident: 10.1016/j.neucom.2016.06.032_bib3 article-title: Improved generalized Atkin algorithm for computing square roots in finite fields publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2005.11.015 – volume: 104 start-page: 297 year: 2006 ident: 10.1016/j.neucom.2016.06.032_bib7 article-title: Construction of Newton-like iteration methods for solving nonlinear equations publication-title: Numer. Math. doi: 10.1007/s00211-006-0025-2 – volume: 167 start-page: 254 year: 2015 ident: 10.1016/j.neucom.2016.06.032_bib15 article-title: A finite-time convergent neural dynamics for online solution of time-varying linear complex matrix equation publication-title: Neurocomputing doi: 10.1016/j.neucom.2015.04.070 – volume: 70 start-page: 513 issue: 1–3 year: 2006 ident: 10.1016/j.neucom.2016.06.032_bib16 article-title: A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network publication-title: Neurocomputing doi: 10.1016/j.neucom.2005.11.006 |
| SSID | ssj0017129 |
| Score | 2.4087296 |
| Snippet | To solve time-varying nonlinear equations, Zhang et al. have developed a one-step discrete-time Zhang dynamics (DTZD) algorithm with O(τ2) error pattern, where... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 516 |
| SubjectTerms | Discrete-time Zhang dynamics Geometric representation Theoretical analysis Three-step algorithm Time-varying nonlinear equations |
| Title | Theoretical analysis, numerical verification and geometrical representation of new three-step DTZD algorithm for time-varying nonlinear equations solving |
| URI | https://dx.doi.org/10.1016/j.neucom.2016.06.032 |
| Volume | 214 |
| WOSCitedRecordID | wos000386741300049&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-8286 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0017129 issn: 0925-2312 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3LjtMwFLWqDgs2vBEzA8gLdiWoSewmWVbM8BIasSiosIn87ENtUjpNNfMpfAj_x3XsuCmDBmbBJqoix45zT32Pr-8DoReJzFQaSxFQzVlATBpCHrI04IoILmSodW3Q__IxOTtLx-PsU6fzs4mF2S6SokgvLrLVfxU13ANhm9DZG4jbdwo34DcIHa4gdrj-q-B9aCJzKUfMhywqeziz6MGUjIOQFb0xnE9UuTSVtUSd5X-1i0iquSQQb1POR6kAELHqnYy-nfTYYlKuZ5vp0ropzpYq2LJ1HTJV2OQbbN1T3yvnaAcz3jY6ct7ki6pAd9Y1JZy1Yrg0SRukQai3TrytSkvzi8n5VLke6mMUe6wyrcrLyuP7qwukYMa_1TV2Fo1wYEL73LrpTJMRDYB37q3SUUha6ywNBy2VTW3Q_RVtYA0T81eFqoxrkBmrTtbqLKp7ybd_U4reVbHxgpvntpfc9JIbZ8AYNP9BlNAs7aKD4fvT8Qd_fJWEkU3y6CbSxGzWjoVX3-bPnKjFc0b30B23QcFDC6z7qKOKB-huU_wDO13wEP1o4Qw3OHuJPcpwG2XQQOIWyvA-ynCpMaAM71CGDcqwRxkGlOE2yrBHGfYoww5lj9DnN6ej1-8CV-cjELBh3QSRJBJoqlEfOoIdgAaSzIEzKcJjKmOgWEJnaawHnJNIRkzBnp31hSJArCinNH6MujCqeoJwxqiSOpJaCEJUKlI5iElMItaXXMqwf4ji5kvnwiXBN7VYFvl1cj5EgX9qZZPA_KV90ggxd0TWEtQckHntk0c3HOkY3d79g56i7mZdqWfolthuZufr5w6WvwC17MvJ |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Theoretical+analysis%2C+numerical+verification+and+geometrical+representation+of+new+three-step+DTZD+algorithm+for+time-varying+nonlinear+equations+solving&rft.jtitle=Neurocomputing+%28Amsterdam%29&rft.au=Guo%2C+Dongsheng&rft.au=Nie%2C+Zhuoyun&rft.au=Yan%2C+Laicheng&rft.date=2016-11-19&rft.issn=0925-2312&rft.volume=214&rft.spage=516&rft.epage=526&rft_id=info:doi/10.1016%2Fj.neucom.2016.06.032&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_neucom_2016_06_032 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-2312&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-2312&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-2312&client=summon |