1995 | OriginalPaper | Chapter
Numerical Solution of Large Finite Markov Chains by Algebraic Multigrid Techniques
Author : Udo R. Krieger
Published in: Computations with Markov Chains
Publisher: Springer US
Included in: Professional Book Archive
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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.