A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
نویسندگان
چکیده
Motivated by the paper [16], where the authors proposed a method to solve a symmetric positive definite (SPD) system Ax = b via a sparse-sparse iterative-based projection method, we extend this method to nonsymmetric linear systems and propose a modified method to construct a sparse approximate inverse preconditioner by using the Frobenius norm minimization technique in this paper. Numerical experiments indicate that this new preconditioner appears more robust and takes less time of constructing than the popular parallel sparse approximate inverse preconditioner (PSM) proposed in [6]
منابع مشابه
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
This paper is concerned with a new approach to preconditioning for large sparse linear systems A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods Some theoretical properties of the preconditioner are discussed a...
متن کاملApproximate Inverse Preconditioning of Iterative Methods for Nonsymmetric Linear Systems
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods. 1. Introduction. We describe a method for computing an incomplete factorization of the inverse of a general sparse matrix A 2 IR nn. The resulting...
متن کاملBlock Approximate Inverse Preconditioners for Sparse Nonsymmetric Linear Systems
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 A0 and the application of the Sherman-MorrisonWoodbury formula to compute an approximate inverse decomposition of...
متن کاملPreconditioning Sparse Nonsymmetric Linear Systems with the Sherman-Morrison Formula
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 A−1 0 −A−1, where A0 is a nonsingular matrix whose inverse is known or easy to compute, can be factorized in the form UΩV T using the Sherman–Morrison formula. When this factorization process is done in...
متن کاملA Sparse Approximate Inverse Preconditioner for Nonsymmetric Positive Definite Matrices
We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylovsubspace-based iterative solvers such as the GMRES algorit...
متن کامل