aI A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively .jarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of

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... an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The paper also contrasts and compares the multi-level method with the iterative aggregation-disaggregation algorithm of Takahashi.