Paper Info
Title
From Davidenko Method to Zhang Dynamics for Nonlinear Equation Systems Solving.
Abstract
The solving of nonlinear equation systems (e.g., complex transcendental dispersion equation systems in waveguide systems) is a fundamental topic in science and engineering. Davidenko method has been used by electromagnetism researchers to solve time-invariant nonlinear equation systems (e.g., the aforementioned transcendental dispersion equation systems). Meanwhile, Zhang dynamics (ZD), which is a special class of neural dynamics, has been substantiated as an effective and accurate method for solving nonlinear equation systems, particularly time-varying nonlinear equation systems. In this paper, Davidenko method is compared with ZD in terms of efficiency and accuracy in solving time-invariant and time-varying nonlinear equation systems. Results reveal that ZD is a more competent approach than Davidenko method. Moreover, discrete-time ZD models, corresponding block diagrams, and circuit schematics are presented to facilitate the convenient implementation of ZD by researchers and engineers for solving time-invariant and time-varying nonlinear equation systems online. The theoretical analysis and results on Davidenko method, ZD, and discrete-time ZD models are also discussed in relation to solving time-varying nonlinear equation systems.
Year
DOI
Venue
2017
10.1109/TSMC.2016.2523917
IEEE Trans. Systems, Man, and Cybernetics: Systems
Keywords
Field
DocType
Nonlinear equations,Mathematical model,Time-varying systems,Newton method,Convergence,Dispersion,Electromagnetics
Convergence (routing),Mathematical optimization,Equation solving,Nonlinear system,Dispersion relation,Mathematical analysis,Electromagnetics,Electromagnetism,Block diagram,Mathematics,Newton's method
Journal
Volume
Issue
ISSN
47
11
2168-2216
Citations 
PageRank 
References 
17
0.68
20
Authors
5
Name
Order
Citations
PageRank
Yunong Zhang12344162.43
Yinyan Zhang2746.95
Dechao Chen38810.75
Zhengli Xiao4433.17
xiaogang yan5373.74