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Technical Note—Accelerated Computation of the Expected Discounted Return in a Markov Chain

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  • Evan L. Porteus

    (Stanford University, Stanford, California)

  • John C. Totten

    (Procter and Gamble Company, Cincinnati, Ohio)

Abstract

This note investigates the use of extrapolations with certain iterative methods to accelerate the computation of the expected discounted return in a finite Markov chain. An easily administered algorithm for reordering the equations allows an attractive stopping rule to be used with Gauss-Seidel iteration. Lower bound and norm reducing extrapolations are introduced. Certain of these extrapolations that are optimal are easily computed. From the results of a small numerical example, it appears that the effects of reordering can be dramatic. Some form of extrapolation with Gauss-Seidel iteration after reordering may turn out to be more efficient in practice than successive over-relaxation.

Suggested Citation

  • Evan L. Porteus & John C. Totten, 1978. "Technical Note—Accelerated Computation of the Expected Discounted Return in a Markov Chain," Operations Research, INFORMS, vol. 26(2), pages 350-358, April.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:2:p:350-358
    DOI: 10.1287/opre.26.2.350
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