More on a Rayleigh-ritz Refinement Technique for Nearly Uncoupled Stochastic Matrices

A Rayleigh-Ritz refinement technique is analyzed that is suitable for accelerating the convergence of iterative procedures for computing the stationary distribution of a nearly uncoupled stochastic matrix. In particular, for that case the error of the new approximation in terms of the previous error and the degree of coupling gets a special form. Cases where the refinement is promising are given as well. All the analysis requires the single assumption that the Markov chain under consideration is irreducible.