On the Variable Step-Size of Discrete-Time Zhang Neural Network and Newton Iteration for Constant Matrix Inversion

Abstract

A special kind of recurrent neural network has recently been proposed by Zhang et al for matrix inversion. Then, for possible hardware and digital-circuit realization, the corresponding discrete-time model of Zhang neural network (ZNN) is proposed for constant matrix inversion, which reduces exactly to Newton iteration when linear activation functions and constat step-size 1 are used. In this paper, a variable step-size choosing method is investigated for such a discrete-time ZNN model, in which different variable step-size rules are derived for different kinds of activation functions. For comparative purposes, the fixed step-size choosing method is presented as well. Numerical examples demonstrate the efficacy of the discrete-time ZNN model, especially when using the variable step-size method.