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Numerical methods in Markov chain modeling

Bernard Philippe 1 Yousef Saad 2 William Stewart 3
1 CALCPAR - Calculateurs Parallèles
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, usually non-symmetric, matrix associated with a known eigenvalue. It can be also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Krylov subspace techniques, single vector power iteration and relaxation procedures, and acceleration techniques. We compare the performance of these methods on some realistic problems.
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Submitted on : Wednesday, May 24, 2006 - 6:13:46 PM
Last modification on : Friday, February 4, 2022 - 3:33:44 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 7:02:12 PM


  • HAL Id : inria-00075444, version 1


Bernard Philippe, Yousef Saad, William Stewart. Numerical methods in Markov chain modeling. [Research Report] RR-1115, INRIA. 1989. ⟨inria-00075444⟩



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