An inverse LU preconditioner based on the Sherman–Morrison formula

Abstract

An approximate inverse LU preconditioner is constructed based on the Sherman–Morrison formula. Applying recursively that inversion formula a multiplicative decomposition of the inverse of a matrix is obtained. This recursion in compact form is the base to build the proposed preconditioner that we call V–AISM. For nonsingular M-matrices and H-matrices of the invertible class the stability of the preconditioner is proved. Numerical results show that V–AISM is robust and competitive compared with other preconditioners.

Keywords

• nonsymmetric linear systems
• iterative methods
• aproximate inverse lu preconditioning
• sherman-morrison formula
• primary 65f08, 65f10
• secondary 65f50