PARALLEL ALGORITHMS AND APPLICATIONS, VOL.6, NO.1, PP.25-37, 1995. TITLE: The Arithmetic Mean Method for Finding the Stationary Vector of Markov Chains AUTHORS: Michele Benzi and Tugrul Dayar ABSTRACT: In this paper we extend the arithmetic mean method for large, sparse systems of linear equations to the case where the coefficient matrix is a singular, irreducible M-matrix. Matrices of this kind arise in the computation of the stationary distribution vector for an irreducible Markov chain, as well as in other applications. We report on some numerical experiments on a simple reliability model, where two forms of the arithmetic mean method are compared. The method is well-suited for parallel implementation on a multiprocessor. KEY WORDS: Singular linear systems, M-matrices, iterative methods, AGE methods, parallel computing, Markov chains, reliability models.