Discrete-time ZD, GD and NI for solving nonlinear time-varying equations

Authors:
Yunong Zhang;Zhen Li;Dongsheng Guo;Zhende Ke;Pei Chen
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China 510006;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China 510006;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China 510006;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China 510006;School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China 510006
Venue:
Numerical Algorithms
Year:
2013

Citing 18
Cited 0

Analog VLSI and neural systems

Analog VLSI and neural systems
A recurrent neural network for real-time matrix inversion

Applied Mathematics and Computation
Linking discrete orthogonality with dilation and translation for incomplete sigma-pi neural networks of Hopfield-type

Discrete Applied Mathematics
Dynamics of a class of discete-time neural networks and their comtinuous-time counterparts

Mathematics and Computers in Simulation
Numerical Methods Using MATLAB

Numerical Methods Using MATLAB
Construction of Newton-like iteration methods for solving nonlinear equations

Numerische Mathematik
Digital Signal Processing

Digital Signal Processing
A Hopfield neural network approach for power optimization of real-time operating systems

Neural Computing and Applications
Fundamental study: Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

Theoretical Computer Science
Simulation and Comparison of Zhang Neural Network and Gradient Neural Network Solving for Time-Varying Matrix Square Roots

IITA '08 Proceedings of the 2008 Second International Symposium on Intelligent Information Technology Application - Volume 02
From Zhang neural network to Newton iteration for matrix inversion

IEEE Transactions on Circuits and Systems Part I: Regular Papers
Solution of nonlinear equations by continuous- and discrete-time Zhang dynamics and more importantly their links to Newton iteration

ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation

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

Numerical Algorithms
Regularized image reconstruction using SVD and a neural networkmethod for matrix inversion

IEEE Transactions on Signal Processing
Convergence analysis of a discrete-time recurrent neural network to perform quadratic real optimization with bound constraints

IEEE Transactions on Neural Networks
A recurrent neural network for solving Sylvester equation with time-varying coefficients

IEEE Transactions on Neural Networks
Design and analysis of a general recurrent neural network model for time-varying matrix inversion

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

A special class of neural dynamics called Zhang dynamics (ZD), which is different from gradient dynamics (GD), has recently been proposed, generalized, and investigated for solving time-varying problems by following Zhang et al.'s design method. In view of potential digital hardware implemetation, discrete-time ZD (DTZD) models are proposed and investigated in this paper for solving nonlinear time-varying equations in the form of $f(x,t)=0$. For comparative purposes, the discrete-time GD (DTGD) model and Newton iteration (NI) are also presented for solving such nonlinear time-varying equations. Numerical examples and results demonstrate the efficacy and superiority of the proposed DTZD models for solving nonlinear time-varying equations, as compared with the DTGD model and NI.