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Preprint 10-2005

Algebraic Multigrid Preconditioners for Computing Stationary Distributions of Markov Processes

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Author(s) : Elena Virnik

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2005

MSC 2000

65F10 Iterative methods for linear systems
65M55 Multigrid methods; domain decomposition

Abstract :
Algebraic Multigrid (AMG) is applied as a preconditioner for solving large linear systems of the type $(I-T^T)x=0$ with GMRES. In this paper $T$ is assumed to be the transition matrix of a Markov process. Thus, in many applications $T$ is singular. Although AMG and GMRES are originally designed for the solution of regular systems, with certain adaptation their applicability can be extended to problems as described above. Furthermore an application of this preconditioning technique to a specific eigenvalue problem is presented.

Keywords : Algebraic Multigrid, preconditioner, large linear systems, Markov

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