Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2015
In this paper we survey our work on preconditioners based on the Inverse Sherman-Morrison factori... more In this paper we survey our work on preconditioners based on the Inverse Sherman-Morrison factorization. The most important theoretical results are also summarized and some numerical conclusions are provided.
In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear syste... more 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 A0 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.
SIAM Journal on Matrix Analysis and Applications, 1995
Let $Ax=b$ be a linear system where $A$ is a symmetric positive definite matrix. Preconditioners ... more Let $Ax=b$ be a linear system where $A$ is a symmetric positive definite matrix. Preconditioners for the conjugate gradient method based on multisplittings obtained by incomplete Choleski factorizations of $A$ are studied. The validity of these preconditioners when $A$ is an $M$-matrix is proved and a parallel implementation is presented.
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2015
In this paper we survey our work on preconditioners based on the Inverse Sherman-Morrison factori... more In this paper we survey our work on preconditioners based on the Inverse Sherman-Morrison factorization. The most important theoretical results are also summarized and some numerical conclusions are provided.
In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear syste... more 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 A0 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.
SIAM Journal on Matrix Analysis and Applications, 1995
Let $Ax=b$ be a linear system where $A$ is a symmetric positive definite matrix. Preconditioners ... more Let $Ax=b$ be a linear system where $A$ is a symmetric positive definite matrix. Preconditioners for the conjugate gradient method based on multisplittings obtained by incomplete Choleski factorizations of $A$ are studied. The validity of these preconditioners when $A$ is an $M$-matrix is proved and a parallel implementation is presented.
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