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

Virnik, Elena

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.