Block iterative algorithms for stochastic matrices
type: Item
instance of: scholarly article
title: Block iterative algorithms for stochastic matrices
zbMATH Open document ID: 0612.65020
DOI: 10.1016/0024-3795(86)90214-4
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: Ist Q die Matrix der Übergangswahrscheinlichkeiten einer endlichen homogenen Markovkette, so entspricht der linke positive Eigenvektor v von Q gerade der stationären Wahrscheinlichkeitsverteilung. Zur Berechnung von v können Varianten der Potenzmethode nach v. Mises angewandt werden; diese beruhen auf Block-Zerlegungen \(I-Q=M-N\) der singulären M- Matrix I-Q (der Iterationsoperator ist dann \(T:=NM^{-1})\). Die vorliegende Arbeit behandelt vor allem den bisher nicht untersuchten Fall, daß T zyklisch ist, obwohl Q irreduzibel ist (bei Blockzerlegungen ist dieses möglich). Es wird gezeigt, wie man speziell beim Block-Jacobi- und Block-Gauß-Seidelverfahren zu einem konvergenten Algorithmus gelangt.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 3990747
zbMATH Keywords: stationary probability distribution vector
zbMATH Keywords: finite homogeneous Markov chain
zbMATH Keywords: regular splittings
zbMATH Keywords: singular M-matrices
zbMATH Keywords: convergence
zbMATH Keywords: iterative decomposition
zbMATH Keywords: aggregation
zbMATH Keywords: Perron-Frobenius eigenvector
zbMATH Keywords: stochastic irreducible matrix
zbMATH Keywords: block Jacobi method
zbMATH Keywords: block Gauß-Seidel method
author: Pierre Courtois
author: Pierre Semal
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90214-4
OpenAlex ID: W1970264501
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Wikidata QID: Q127678948
description: scientific article; zbMATH DE number 3990747