Alternative numerical approaches for solving matrix equations associated with M/G/1-type Markov chains are considered in this chapter. A general shift technique for accelerating the convergence of iterative methods is described, and its application to accelerating cyclic reduction is analysed. A functional iteration relying on the combination of cyclic reduction and fixed point iteration is introduced: its convergence is linear but its convergence rate can be arbitrarily large. A doubling method, evaluation interpolation techniques, and the invariant subspace method complete the chapter.
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