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

Elena Virnik | Zendy

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

Author(s) -

Elena Virnik

Publication year - 2007

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/060659272

Subject(s) - preconditioner , generalized minimal residual method , mathematics , multigrid method , linear system , algebraic number , matrix (chemical analysis) , mathematical analysis , partial differential equation , materials science , composite material

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.

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