Preconditioning Highly Indefinite and Nonsymmetric Matrices

Standard preconditioners, like incomplete factorizations, perform well when the coeecient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutations and scalings aimed at placing large entries on the diagonal in the context of preconditioning for general sparse matrices. We target highly indeenite, nonsymmetric problems which cause diiculties for preconditioned iterative solvers. Our numerical experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing. 1. Introduction. 1.1. Motivation and focus. We consider the solution of sparse linear systems Ax = b, where A is a general sparse n n nonsingular matrix, by preconditioned