A Two-Stage Iteration for Solving Nearly Uncoupled Markov Chains
Stewart, G. W.
Stewart, W. J.
McAllister, D. F.
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This paper is concerned with an iteration for determining the steady-state probability vector of a nearly uncoupled Markov Chain. The states of these chains can be partitioned into aggregates with low probabilities of transitions between aggregates. The iteration consists of alternating block Gauss--Seidel iterations with Rayleigh--Ritz refinements. Under natural regularity conditions, the composite iteration reduces the error by a factor proportional to the size of the coupling between aggregates, so that the more loosely the chain is coupled, the faster the convergence.