A Sparse Approximate Inverse Preconditioner For The Conjugate Gradient Method

. A method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix A is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations. It is proved that in exact arithmetic the preconditioner is well defined if A is an H-matrix. The results of numerical experiments are presented. Key words. sparse approximate inverses, preconditioned conjugate gradient method, Hmatrices, incomplete factorizations AMS subject classifications. 65F10, 65F35, 65F50, 65Y05 1. Introduction. In this paper we develop a method for computing an incomplete factorization of the inverse of a symmetric positive definite (SPD) matrix A . The resulting factorized sparse approximate inverse is used as an explicit preconditioner for the solution of Ax = b by the preconditioned conjugate gradient (PCG) method. Due to the fact that an explicit preconditioning step only requires matrix-- vector prod..