The monotone convergence rate of the parallel nonlinear AOR method
type: Item
instance of: scholarly article
title: The monotone convergence rate of the parallel nonlinear AOR method
zbMATH Open document ID: 0851.65026
DOI: 10.1016/0898-1221(96)00013-2
publication date: 1996-11-26T00:00:00Z
review text: Systems of nonlinear equations (1) \(Ax+ \varphi(x)= b\) are solved iteratively using a combination of an accelerated overrelaxation (AOR) and a multisplitting method. The resulting algorithm is called ``Parallel nonlinear AOR method'' by the author. In (1) \(A\) is a real nonsingular \(n\times n\) matrix, \(b\), \(x= (x_i)\in \mathbb{R}^n\) are vectors and \(\varphi= (\varphi_i): \mathbb{R}^n\to \mathbb{R}^n\) is a continuous, diagonal and isotone function where diagonal means that \(\varphi_i\) depends on \(x_i\) only. For \(M\)-matrices \(A\) conditions on the underlying splittings and on the AOR-parameters are listed for the sequence \(\{x^m\}\) of iterates to converge to the unique solution of (1). Moreover, a comparison result is proved and a numerical example is given.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 880524
zbMATH Keywords: monotone convergence rate
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: parallel computation
zbMATH Keywords: accelerated overrelaxation
zbMATH Keywords: multisplitting method
zbMATH Keywords: \(M\)-matrices
zbMATH Keywords: numerical example
author: Zhong-Zhi Bai
reviewed by: Günter Mayer
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00013-2
OpenAlex ID: W2051047195
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 880524