Block approximate inverse preconditioners for sparse nonsymmetric linear systems

J. Cerdán, T. Faraj, N. Malla, J. Marín, and J. Mas

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 $A_0$ 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 that 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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Key words

approximate inverse preconditioners, variable rank updates, block algorithms, Krylov iterative methods, Sherman-Morrison-Woodbury formula

AMS subject classifications

65F10, 65F35, 65F50

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