Comparison on continuous-time zhang dynamics and Newton-Raphson iteration for online solution of nonlinear equations

Authors:
Yunong Zhang;Zhende Ke;Zhan Li;Dongsheng Guo
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China
Venue:
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Year:
2011

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Abstract

Our previous work has shown the efficacy and promising performance of continuous-time Zhang dynamics (CTZD) for solving online nonlinear equations, as compared with conventional gradient dynamics (GD). It has also shown that, with linear activation functions used and with step-size being 1, the discrete-time Zhang dynamics (DTZD) reduces to the Newton-Raphson iteration (NRI) (i.e., being a special case of the DTZD model) for static nonlinear equations solving. It is known that the NRI may fail to converge to the theoretical roots of some difficult or special problems. In this paper, the CTZD model and NRI method are investigated comparatively for online solution of static nonlinear equations by performing numerical tests in different situations. Computer testing and simulation results further demonstrate the efficacy and different convergence-performance of the CTZD model (activated by a power-sigmoid function) and NRI for nonlinear equations solving.