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

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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

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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