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Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques

In: Computations with Markov Chains

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  • Udo R. Krieger

    (Deutsche Bundespost Telekom Research and Technology Centre)

Abstract

Iterative aggregation/disaggregation procedures are a convenient numerical solution method for computing the stationary distribution vector of an ergodic homogeneous Markov chain with a finite state space. We show the equivalence of this method and a two-level multigrid method. Based on error results of the A/D-method, we provide an error analysis of an efficient multigrid variant of the multiplicative Schwars-iteration method. Furthermore, we apply these results to a multigrid version of the replacement process approach developed by Sumita and Rieders.

Suggested Citation

  • Udo R. Krieger, 1995. "Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 23, pages 403-424, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_23
    DOI: 10.1007/978-1-4615-2241-6_23
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