From Zhang Neural Network to Newton Iteration for Matrix Inversion

Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang 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...

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Vydané v:IEEE transactions on circuits and systems. I, Regular papers Ročník 56; číslo 7; s. 1405 - 1415
Hlavní autori: Yunong Zhang, Yunong Zhang, Weimu Ma, Weimu Ma, Binghuang Cai, Binghuang Cai
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.07.2009
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Activation function
Control systems
Convergence
Difference equations
Dynamics
Error functions
initial state
Inversions
Iterative methods
Mathematical models
matrix inversion
Neural networks
Newton iteration
On-line systems
Online
recurrent neural network (RNN)
Recurrent neural networks
Robot control
Signal processing algorithms
Stability
Statistics
step size
Studies
ISSN:1549-8328, 1558-0806
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Popis
Shrnutí:Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang 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.
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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2008.2007065