Theoretical analysis, numerical verification and geometrical representation of new three-step DTZD algorithm for time-varying nonlinear equations solving

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• 作者：Dongsheng Guo ; ^{gdongsh@hqu.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Zhuoyun NieAuthor Vitae ; Laicheng YanAuthor Vitae
• 关键词：Discrete-time Zhang dynamics ; Three-step algorithm ; Geometric representation ; Theoretical analysis ; Time-varying nonlinear equations
• 刊名：Neurocomputing
• 出版年：2016
• 出版时间：19 November 2016
• 年：2016
• 卷：214
• 期：Complete
• 页码：516-526
• 全文大小：2100 K

文摘

To solve time-varying nonlinear equations, Zhang et al. have developed a one-step discrete-time Zhang dynamics (DTZD) algorithm with O(τ²)$O\left({\tau }^2\right)$ 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)$O\left({\tau }^3\right)$ 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.