Perturbation results for nearly uncoupled Markov chains with applications to iterative methods

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The standard perturbation theory for linear equations states that nearly uncoupled Markov chains (NUMCs) are very sensitive to small changes in the elements. Indeed, some algorithms, such as standard Gaussian elimination, will obtain poor results for such problems. A structured perturbation theory is given that shows that NUMCs usually lead to well conditioned problems. It is shown that with appropriate stopping, criteria, iterative aggregation/disaggregation algorithms will achieve these structured error bounds. A variant of Gaussian elimination due to Grassman, Taksar and Heyman was recently shown by O'Cinneide to achieve such bounds.

Original languageEnglish (US)
Pages (from-to)51-62
Number of pages12
JournalNumerische Mathematik
Volume65
Issue number1
DOIs
StatePublished - Dec 1 1993

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Gaussian elimination
Iterative methods
Markov processes
Perturbation Theory
Markov chain
Structured Perturbations
Perturbation
Iteration
Disaggregation
Stopping Criterion
Linear equations
Error Bounds
Linear equation
Aggregation
Agglomeration
Standards

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Perturbation results for nearly uncoupled Markov chains with applications to iterative methods. / Barlow, Jesse L.

In: Numerische Mathematik, Vol. 65, No. 1, 01.12.1993, p. 51-62.

Research output: Contribution to journalArticle

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