From Zhang Neural Network to Newton Iteration for Matrix Inversion

Zhang, Y; Ma, W; Cai, B

From Zhang Neural Network to Newton Iteration for Matrix Inversion

Zhang, Y Ma, W Cai, B

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Publisher:: IEEE
Publication Type:: Journal Article
Citation:: IEEE Transactions on Circuits and Systems I - Regular Papers, 2009, 56 (7), pp. 1405 - 1415
Issue Date:: 2009-01

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Field	Value	Language
dc.contributor.author	Zhang, Y	en_US
dc.contributor.author	Ma, W	en_US
dc.contributor.author	Cai, B	en_US
dc.date.issued	2009-01	en_US
dc.identifier.citation	IEEE Transactions on Circuits and Systems I - Regular Papers, 2009, 56 (7), pp. 1405 - 1415	en_US
dc.identifier.issn	1549-8328	en_US
dc.identifier.uri	http://hdl.handle.net/10453/15241
dc.description.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.	en_US
dc.publisher	IEEE	en_US
dc.relation.ispartof	IEEE Transactions on Circuits and Systems I - Regular Papers	en_US
dc.relation.isbasedon	10.1109/TCSI.2008.2007065	en_US
dc.rights	© 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.subject.classification	Electrical & Electronic Engineering	en_US
dc.title	From Zhang Neural Network to Newton Iteration for Matrix Inversion	en_US
dc.type	Journal Article
utslib.citation.volume	7	en_US
utslib.citation.volume	56	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.consider-herdc	false	en_US
pubs.issue	7	en_US
pubs.volume	56	en_US

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.

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http://hdl.handle.net/10453/15241