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

✍ Scribed by Wilhelm Niethammer

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 321 KB
Volume: 287
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10102-7

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✦ Synopsis

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) showed together with other results that for p-periodic Markov chains convergence of SOR in an extended sense can happen for m ¢ (0, 2). The purpose of this note is to show how this astonishing result can be derived comparatively easy for twoperiodic Markov chains from the well-known convergence properties of power iteration.

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