Entrywise perturbation theory and error analysis for Markov chains
type: Item
instance of: scholarly article
title: Entrywise perturbation theory and error analysis for Markov chains
zbMATH Open document ID: 0804.65145
DOI: 10.1007/BF01385743
author: Colm Art O'Cinneide
published in: Numerische Mathematik
publication date: 1994-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/133726
review text: \textit{W. K. Grassmann}, \textit{M. I. Taksar} and \textit{D. P. Heyman} [Oper. Res. 33, 1107-1116 (1985; Zbl 0576.60083)] introduced a variant of Gaussian elimination for computing the steady-state vector of a Markov chain. The present author proves that their algorithm is stable, and that the problem itself is well-conditioned. The key to the analysis is to focus on entrywise relative error in both the data and the computed solution.
reviewed by: F. Zhang
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 569120
zbMATH Keywords: entrywise perturbation
zbMATH Keywords: error analysis
zbMATH Keywords: numerical stability
zbMATH Keywords: well- conditioned problem
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: Markov chain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 569120