A new preconditioning technique for solving large sparse linear systems

A new sparse approximate triangular factorization technique for solving large sparse linear system by iterative methods is proposed. The method is based on the description of the triangular factorization of a matrix as a product of elementary matrices and provides a general scheme for constructing incomplete preconditioners for the given matrix. In particular, the familiar incomplete Choleski decomposition can be incorporated into this scheme. The algorithm, based on choice by value, compares favorably with the incomplete Choleski preconditioner and, equipped with a user-controlled parameter, is able to tackle extremely ill-conditioned problems arising in structural analysis, semiconductor simulation, oil-reservoir modelling, and other applications. When applied to a positive definite symmetric matrix, the algorithm produces a preconditioning matrix preserving that property. © 1991.