Summary
The conjugate gradient method is developed for computing stationary probability vectors of a large sparse stochastic matrixP, which often arises in the analysis of queueing system. When unit vectors are chosen as the initial vectors, the iterative method generates all the extremal probability vectors of the convex set formed by all the stationary probability vectors ofP, which are expressed in terms of the Moore-Penrose inverse of the matrix (P−I). A numerical method is given also for classifying the states of the Markov chain defined byP. One particular advantage of this method is to handle a very large scale problem without resorting to any special form ofP.
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Tanabe, K. The conjugate gradient method for computing all the extremal stationary probability vectors of a stochastic matrix. Ann Inst Stat Math 37, 173–187 (1985). https://doi.org/10.1007/BF02481090
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DOI: https://doi.org/10.1007/BF02481090