A SPARSE APPROXIMATE INVERSE PRECONDITIONER FOR NONSYMMETRIC LINEAR-SYSTEMS

This paper is concerned with a new approach to preconditioning for lar ge, sparse linear systems. A procedure for computing an incomplete fac torization of the inverse of a nonsymmetric matrix is developed, and t he resulting factorized sparse approximate inverse is used as an expli cit preconditioner for conjugate gradient-type methods. Some theoretic al properties of the preconditioner are discussed, and numerical exper iments on test matrices from the Harwell-Boeing collection and from Ti m Davis's collection are presented. Our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners. Furthermore, the new technique insures convergence ra tes of the preconditioned iteration which are comparable with those ob tained with standard implicit preconditioners.