Matrix splitting principles
type: Item
instance of: scholarly article
title: Matrix splitting principles
zbMATH Open document ID: 1005.65029
DOI: 10.1155/S0161171201007062
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49770
full work available at URL: S0161171201007062.html
review text: The author discusses the solution of systems of linear equations \(Ax = b\) by means of iterative methods based on matrix splittings \(A = M - N\) with a nonsingular matrix \(M\). The author gives a definition of a regular, nonnegative, weak nonnegative, weak, weaker and convergent splitting of \(A\). A systematic analysis of convergence conditions used in comparison theorems is presented. A scheme of condition implications for regular splittings of \(A = M_1 - N_1 = M_2 - N_2\), where \(A^{-1} \geq 0\), is given. Furthermore, nonnegative and weak nonnegative splittings as well as weak and weaker splittings are analysed in detail.
reviewed by: Michael Jung
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1780266
zbMATH Keywords: systems of linear algebraic equations
zbMATH Keywords: iterative methods
zbMATH Keywords: matrix splitting
zbMATH Keywords: regular splitting
zbMATH Keywords: nonnegative splitting
zbMATH Keywords: weak splitting
zbMATH Keywords: convergent splitting
zbMATH Keywords: comparison theorems
zbMATH Keywords: convergence
author: Zbigniew I. Woźnicki
MaRDI profile type: Publication
OpenAlex ID: W2033384536
description: scientific article; zbMATH DE number 1780266