An Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices

An Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices

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 were originally designed for the solution of regular systems, with adequa...

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Veröffentlicht in:SIAM journal on scientific computing 2007-01, Vol.29 (5), p.1982-1991
1. Verfasser: Virnik, Elena
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Eigenvalues
Eigenvectors
Markov analysis
Probability
Probability distribution
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Zusammenfassung: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 were originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to problems as described above.
ISSN:1064-8275
1095-7197
DOI:10.1137/060659272