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.