Approximate Inverse Preconditioning of Iterative Methods for Nonsymmetric Linear Systems

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 factorized sparse approximate inverse, which is guaranteed to exist if A is an H-matrix, can be used as an explicit preconditioner for the solution of Ax = b by conjugate gradient-type methods. The application of the preconditioner only requires matrix-vector products, which can be advantageous on vector and parallel architectures. In contrast, implicit preconditioners (such as ILU) involve the solution of triangular linear systems, whose eecient implementation can be problematic in a parallel environment. The results of our experiments with a sequential implementation of the new method indicate that the approximate inverse preconditioner results in good convergence rates (comparable to those obtained with standard ILU techniques). A detailed study of this method can be found in 3].