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On a direct method for the solution of nearly uncoupled Markov chains

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Summary

This note is concerned with the accuracy of the solution of nearly uncoupled Markov chains by a direct method based on the LU decomposition. It is shown that plain Gaussian elimination may fail in the presence of rounding errors. A modification of Gaussian elimination with diagonal pivoting and correction of small pivots is proposed and analyzed. It is shown that the accuracy of the solution is affected by two condition numbers associated with aggregation and the coupling respectively.

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Authors and Affiliations

  1. Department of Computer Science, University of Maryland, 20742, College Park, MD, USA

    G. W. Stewart

  2. Institute for Advanced Computer Studies, University of Maryland, 20742, College Park, MD, USA

    G. W. Stewart & G. Zhang

Authors
  1. G. W. Stewart
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  2. G. Zhang
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Additional information

This work was supported in part by the Air Force Office of Sponsored Research under Contract AFOSR-87-0188

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Stewart, G.W., Zhang, G. On a direct method for the solution of nearly uncoupled Markov chains. Numer. Math. 59, 1–11 (1991). https://doi.org/10.1007/BF01385767

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  • DOI: https://doi.org/10.1007/BF01385767

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