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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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
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