Abstract. We introduce a new iterative method 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. 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.

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