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...

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) Vol. 214; pp. 516 - 526
Main Authors: Guo, Dongsheng, Nie, Zhuoyun, Yan, Laicheng
Format: Journal Article
Language:English
Published: Elsevier B.V 19.11.2016
Subjects:
Discrete-time Zhang dynamics
Geometric representation
Theoretical analysis
Three-step algorithm
Time-varying nonlinear equations
Time-varying nonlinear equations
Theoretical analysis
Discrete-time Zhang dynamics
Three-step algorithm
Geometric representation
ISSN:0925-2312, 1872-8286
Online Access:Get full text
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Summary: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.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2016.06.032