Approximate Inverse Preconditioning of Iterative Methods for Nonsymmetric Linear Systems M. Benzi CERFACS, Toulouse France and M. Tuma Institute of Computer Science, Prague, Czech Republic Abstract 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.