Further Comparisons of Direct Methods for Computing Stationary Distributions of Markov Chains

Abstract

An algorithm for computing the stationary distribution of an irreducible Markov chain consisting of ergodic states is described in Grassmann et al. [Oper. Res., 33 (1985), pp. 1107–1116]. In this algorithm, all the arithmetic operations use only nonnegative numbers and there are no subtractions. In this paper we present numerical evidence to show that this algorithm achieves significantly greater accuracy than other algorithms described in the literature. We also describe our computational experience with large block-tridiagonal matrices.