From Zhang neural network to Newton iteration for matrix inversion

Authors:
Yunong Zhang;Weimu Ma;Binghuang Cai
Affiliations:
Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou, China;Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou, China;Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou, China
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2009

Citing 12
Cited 12

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Abstract

Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang et al. for online matrix inversion. Such an RNN is designed based on a matrix-valued error function instead of a scalar-valued error function. In addition, it was depicted in an implicit dynamics instead of an explicit dynamics. In this paper, we develop and investigate a discrete-time model of Zhang neural network (termed as such and abbreviated as ZNN for presentation convenience), which is depicted by a system of difference equations. Comparing with Newton iteration for matrix inversion, we find that the discrete-time ZNN model incorporates Newton iteration as its special case. Noticing this relation, we perform numerical comparisons on different situations of using ZNN and Newton iteration for matrix inversion. Different kinds of activation functions and different step-size values are examined for superior convergence and better stability of ZNN. Numerical examples demonstrate the efficacy of both ZNN and Newton iteration for online matrix inversion.