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Relaxed functional iteration techniques for the numerical solution of M/G/1 type Markov chains

Authors:	Paola Favati Beatrice Meini

Institution:	(1) Istituto di Matematica Computazionale del C.N.R., via S. Maria 46, I-56127 Pisa, Italy;(2) Dipartimento di Matematica, via Buonarroti 2, I-56127 Pisa, Italy

Abstract:	We introduce a new iterative method for the computation of the minimal nonnegative solutionG of the matrix equation $X = \sum\nolimits_{i = 0}^{ + \infty } {X^i A_i }$ , arising in the numerical solution of M/G/1 type Markov chains. The idea consists in applying a relaxation technique to customarily used functional iteration formulas. The proposed method is easy to implement and outperforms, in terms of number of iterations and execution time, the standard functional iteration techniques.

Keywords:	65U05 65F15 15A51 15A24 60J10 60K25
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