Algebraic Schwarz methods for the numerical solution of Markov chains
type: Item
instance of: scholarly article
title: Algebraic Schwarz methods for the numerical solution of Markov chains
zbMATH Open document ID: 1050.65030
author: Ivo Marek
author: Daniel B. Szyld
published in: Linear Algebra and its Applications
publication date: 2004-08-04T00:00:00Z
review text: The authors propose an iterative method to solve singular linear systems. They use the additive and multiplicative Schwarz method to solve large sparse singular linear systems of the form \(Ax=b\), where \(A\) is a singular M-matrix, which means that \(A=I-B\) and \(B\) is nonnegative stochastic matrix. In particular, they consider the case \(b=0\), which corresponds to the stationary probability of a Markov chain represented by \(B\). They show that the multiplicative Schwarz iterations is convergent.
reviewed by: Khalil Ezzinbi
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65C40
Mathematics Subject Classification ID: 60J22
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 2081257
zbMATH Keywords: Schwarz methods
zbMATH Keywords: singular M-matrices
zbMATH Keywords: Markov chains
zbMATH Keywords: stationary probability vectors
zbMATH Keywords: iterative methods
zbMATH Keywords: sparse matrices
zbMATH Keywords: convergence
zbMATH Keywords: stochastic matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.046
OpenAlex ID: W2109044896
Wikidata QID: Q115156460
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DOI: 10.1016/J.LAA.2003.12.046
description: scientific article; zbMATH DE number 2081257