A note on the extended convergence of SOR for two-periodic Markov chains Original Research Article

It is well known that successive overrelaxation (SOR) can be used to compute the stationary distribution of a homogeneous Markov chain. In a long paper Kontovasalis et al. (K. Kontovasalis, R.J. Plemmons, W.J. Stewart, Linear Algebra Appl. 154–156 (1991) 145–223) showed together with other results that for p-periodic Markov chains convergence of SOR in an extended sense can happen for ω negated set membership (0. 2). The purpose of this note is to show how this astonishing result can be derived comparatively easy for two-periodic Markov chains from the well-known convergence properties of power iteration.