Summary.
By performing an accurate analysis of the convergence, we give a complete theoretical explanation of the experimental behaviour of functional iteration techniques for the computation of the minimal nonnegative solution \(G\) of the matrix equation \(X=\sum_{i=0}^{+\infty}X^iA_i\), arising in the numerical solution of M/G/1 type Markov chains (here the \(A_i\)'s are nonnegative \(k\times k\) matrices such that the matrix \(\sum_{i=0}^{+\infty}A_i\) is column stochastic). Moreover, we introduce a general class of functional iteration methods, which includes the standard methods, and we give an optimality convergence result in this class.
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Received September 1, 1995 / Revised version received September 9, 1996
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Meini, B. New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains. Numer. Math. 78, 39–58 (1997). https://doi.org/10.1007/s002110050303
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DOI: https://doi.org/10.1007/s002110050303