A numerical method for a direct obstacle scattering problem
Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
A numerical method for a direct obstacle scattering problem
Applied Numerical Mathematics - Applied scientific computing: Recent approaches to grid generation, approximation and numerical modelling
A Sherman-Morrison approach to the solution of linear systems
Journal of Computational and Applied Mathematics
Greville's method for preconditioning least squares problems
Advances in Computational Mathematics
Improved Balanced Incomplete Factorization
SIAM Journal on Matrix Analysis and Applications
Parallel implementation of the sherman-morrison matrix inverse algorithm
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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Let Ax=b be a large, sparse, nonsymmetric system of linear equations. A new sparse approximate inverse preconditioning technique for such a class of systems is proposed. We show how the matrix A0-1 - A-1, where A0 is a nonsingular matrix whose inverse is known or easy to compute, can be factorized in the form $U\Omega V^T$ 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 A0=sIn, where In 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.