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2010•ETNA - Electronic Transactions on Numerical AnalysisRequires access

BLOCK APPROXIMATE INVERSE PRECONDITIONERS FOR SPARSE NONSYMMETRIC LINEAR SYSTEMS

Juana Mercedes Cerdán Soriano, Táher Faraj El Guelei, Natalia Malla Martínez, J. Marı́n, J. Mas

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Abstract

In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear systems with iterative Krylov subspace methods are studied. The computation of the preconditioners involves consecutive updates of variable rank of an initial and nonsingular matrix and the application of the Sherman-Morrison- Woodbury formula to compute an approximate inverse decomposition of the updated matrices. Therefore, they are generalizations of the preconditioner presented in Bru et al. (SIAM J. Sci. Comput., 25 (2003), pp. 701-715). The stability of the preconditioners is studied and it is shown t hat their computation is breakdown-free for H-matrices. To test the performance the results of numerical experiments obtained for a representative set of matrices are presented.

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What this paper is about

In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear systems with iterative Krylov subspace methods are studied. The computation of the preconditioners involves consecutive updates of variable rank of an initial and nonsingular matrix and the application of the Sherman-Morrison- Woodbury formula to compute an approximate inverse decomposition of the updated matrices. Therefore, they are generalizations of the preconditioner presented in Bru et al. (SIAM J. Sci. Comput., 25 (2003), pp. 701-715). The stability of the preconditioners is studied and it is shown t hat their computation is breakdown-free for H-matrices. To test the performance the results of numerical experiments obtained for a representative set of matrices are presented.

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Available abstract

In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear systems with iterative Krylov subspace methods are studied. The computation of the preconditioners involves consecutive updates of variable rank of an initial and nonsingular matrix and the application of the Sherman-Morrison- Woodbury formula to compute an approximate inverse decomposition of the updated matrices. Therefore, they are generalizations of the preconditioner presented in Bru et al. (SIAM J. Sci. Comput., 25 (2003), pp. 701-715). The stability of the preconditioners is studied and it is shown t hat their computation is breakdown-free for H-matrices. To test the performance the results of numerical experiments obtained for a representative set of matrices are presented.

Key concepts: Preconditioner, Mathematics, Invertible matrix, Krylov subspace, Linear system, Inverse, Applied mathematics, Block matrix

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BLOCK APPROXIMATE INVERSE PRECONDITIONERS FOR SPARSE NONSYMMETRIC LINEAR SYSTEMS — Research Paper | ScholarLens