Improving Jacobi methods for nonnegative \(H\)-matrices linear systems
type: Item
instance of: scholarly article
title: Improving Jacobi methods for nonnegative \(H\)-matrices linear systems
zbMATH Open document ID: 1120.65037
author: Ting-Zhu Huang
author: Xuezhong Wang
author: Ying-Ding Fu
published in: Applied Mathematics and Computation
publication date: 2007-06-06T00:00:00Z
review text: The authors generalize results of \textit{Y. Zhang, T.-Z. Huang} and \textit{X.-P. Liu} [Comput.\ Math.\ Appl. 50, No.~10--12, 1587--1602 (2005; Zbl 1087.65031)] for linear systems whose matrix is a nonnegative \(H\)-matrix. The main idea is to construct a preconditioner \(P\) for the Jacobi method. This \(P\) takes the form of the identity matrix with one nonzero off-diagonal element per row. The position and the value of these off-diagonal elements are chosen so as to optimize the convergence, i.e., to minimize the spectral radius of the iteration matrix.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 5162010
zbMATH Keywords: \(H\)-matrix
zbMATH Keywords: Jacobi type iteration
zbMATH Keywords: precondition
zbMATH Keywords: convergence
zbMATH Keywords: spectral radius
zbMATH Keywords: iteration matrix
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
full work available at URL: j.amc.2006.07.133
OpenAlex ID: W2040027612
cites work: Modified iterative methods for nonnegative matrices and \(M\)-matrices linear systems
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cites work: More on modifications and improvements of classical iterative schemes for \(M\)-matrices
cites work: On Accelerated Iterative Methods for the Solution of Systems of Linear Equations
cites work: Modified iterative methods for consistent linear systems
DOI: 10.1016/J.AMC.2006.07.133
description: scientific article; zbMATH DE number 5162010