We present a block version of the SPAI algorithm and test its performance on large nonsymmetric matrices in a parallel environment. The SPAI algorithm, initially proposed by Grote and Huckle 1], computes a SParse Approximate Inverse for use as a preconditioner for the iterative solution of a sparse linear system of equations. It has proved to be a robust and versatile preconditioner in numerous...

In this paper, we study the use of an incomplete Cholesky factorization (ICF) as a preconditioner for solving dense symmetric positive definite linear systems. This method is suitable for situations where matrices cannot be explicitly stored but each column can be easily computed. Analysis and implementation of this preconditioner are discussed. We test the proposed ICF on randomly generated sy...

This paper presents a class of preconditioning techniques which exploit rational function approximations to the original matrix. The matrix is rst shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner to the original matrix. Since the incomplete factorization is made on a shifted matrix, a good...

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...

Direct methods have made remarkable progress in the computational efficiency of factorization algorithms during the last three decades. The advances in graph theoretic algorithms have not received enough attention from the iterative methods community. For example, we demonstrate how symbolic factorization algorithms from direct methods can accelerate the computation of a factored approximate in...

When solving large linear systems of equations arising from the discretization of elliptic boundary value problems, a combination of iterative methods and preconditioners based on incomplete LU factorizations is frequently used. Given a model problem with variable coefficients, we investigate a class of incomplete LU factorizations depending on a relaxation parameter. We show that the associate...

In this paper an approach is proposed for preconditioning large general sparse matrices. This approach combines the scalability of explicit preconditioners with the preconditioning eeciency of incomplete factorizations. Several algorithms resulting from this approach are presented. Both the preconditioning eeciency and the cost of applying this preconditioner are tested. The experiments indicat...

Incomplete LDL∗ factorizations sometimes produce an inde nite preconditioner even when the input matrix is Hermitian positive de nite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive de nite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can b...

We propose variants of the modified incomplete Cholesky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

For general symmetric positive definite (SPD) matrices, we present a framework for designing effective and robust black-box preconditioners via structured incomplete factorization. In a scaling-and-compression strategy, off-diagonal blocks are first scaled on both sides (by the inverses of the factors of the corresponding diagonal blocks) and then compressed into low-rank approximations. ULV-ty...