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Continuous and discrete time Zhang dynamics for time-varying 4th root finding

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Abstract

Recently, a special class of neural dynamics has been proposed by Zhang et al. for online solution of time-varying and/or static nonlinear equations. Different from eliminating a square-based positive error-function associated with gradient-based dynamics (GD), the design method of Zhang dynamics (ZD) is based on the elimination of an indefinite (unbounded) error-function. In this paper, for the purpose of online solution of time-varying 4th root, both continuous-time ZD (CTZD) and discrete-time ZD (DTZD) models are developed and investigated. In addition, power-sigmoid activation function is exploited in Zhang dynamics, which makes ZD models possess the property of superior convergence and better accuracy. To summarize generalization for possible widespread application, such approach is further extended to general time-varying nonlinear equations solving. Computer-simulation results demonstrate the efficacy of the ZD models for finding online time-varying 4th root and solving general time-varying equations.

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Authors and Affiliations

  1. School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, 510006, China

    Yunong Zhang, Lin Xiao, Gongqin Ruan & Zhan Li

Authors
  1. Yunong Zhang
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  2. Lin Xiao
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  3. Gongqin Ruan
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  4. Zhan Li
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Corresponding author

Correspondence to Yunong Zhang.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant 60775050, the Program for New Century Excellent Talents in University (NCET-07-0887), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.

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Zhang, Y., Xiao, L., Ruan, G. et al. Continuous and discrete time Zhang dynamics for time-varying 4th root finding. Numer Algor 57, 35–51 (2011). https://doi.org/10.1007/s11075-010-9410-0

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  • DOI: https://doi.org/10.1007/s11075-010-9410-0

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