A sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of an SPD matrix

Abstract

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a preconditioner for solving symmetric positive definite linear systems of equations by using the preconditioned conjugate gradient algorithm. Some numerical experiments on test matrices from the Harwell–Boeing collection for comparing the numerical performance of the presented method with one available well-known algorithm are also given.