Preconditioning sparse nonsymmetric linear systems with the Sherman-Morrison formula

被引:30
|
作者
Bru, R [1 ]
Cerdán, J [1 ]
Marín, J [1 ]
Mas, J [1 ]
机构
[1] Univ Politecn Valencia, Dept Matemat Aplicada, Valencia 46022, Spain
来源
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2003年 / 25卷 / 02期
关键词
nonsymmetric linear systems; factorized sparse approximate inverses; Sherman-Morrison formula; preconditioned iterative methods;
D O I
10.1137/S1064827502407524
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let Ax = b be a large, sparse, nonsymmetricsystem of linear equations. A new sparse approximate inverse preconditioning technique for such a class of systems is proposed. We show how the matrix A(0)(-1) - A(-1), where A(0) is a nonsingular matrix whose inverse is known or easy to compute, can be factorized in the form UOmegaV(T) using the Sherman - Morrison formula. When this factorization process is done incompletely, an approximate factorization may be obtained and used as a preconditioner for Krylov iterative methods. For A(0) = sI(n), where I-n is the identity matrix and s is a positive scalar, the existence of the preconditioner for M-matrices is proved. In addition, some numerical experiments obtained for a representative set of matrices are presented. Results show that our approach is comparable with other existing approximate inverse techniques.
引用
收藏
页码:701 / 715
页数:15
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