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Computations with Markov Chains pp 403–424Cite as

Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques

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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.

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Author information

Authors and Affiliations

  1. Deutsche Bundespost Telekom Research and Technology Centre, Am Kavalleriesand 3, D-64295, Darmstadt, Germany

    Udo R. Krieger

Authors
  1. Udo R. Krieger
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Editor information

Editors and Affiliations

  1. North Carolina State University, Raleigh, NC, USA

    William J. Stewart

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© 1995 Springer Science+Business Media New York

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Krieger, U.R. (1995). Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques. In: Stewart, W.J. (eds) Computations with Markov Chains. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2241-6_23

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  • DOI: https://doi.org/10.1007/978-1-4615-2241-6_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5943-2

  • Online ISBN: 978-1-4615-2241-6

  • eBook Packages: Springer Book Archive

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