Preprint 03-2006

An Algebraic Multigrid Preconditioner for a class of singular M-Matrices

Author(s) : Elena Virnik

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 03-2006

MSC 2000

65F10 Iterative methods for linear systems

65M55 Multigrid methods; domain decomposition

Abstract :
We apply Algebraic Multigrid (AMG) as a preconditioner for solving large singular linear systems of the type $(I-T^T)x=0$ with GMRES. Here, $T$ is assumed to be the transition matrix of a Markov process. Although AMG and GMRES are originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to problems as described above.

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