A New GMRES(m)‎ Method for Markov Chains

Abstract EN

This paper presents a class of new accelerated restarted GMRES method for calculating the stationary probability vector of an irreducible Markov chain.

We focus on the mechanism of this new hybrid method by showing how to periodically combine the GMRES and vector extrapolation method into a much efficient one for improving the convergence rate in Markov chain problems.

Numerical experiments are carried out to demonstrate the efficiency of our new algorithm on several typical Markov chain problems.