Preconditioning highly indefinite and nonsymmetric matrices

Standard preconditioners, like incomplete factorizations, perform well when the coefficient matrix is diagonally dominant, but often fail on general s parse matrices. We experiment with nonsymmetric permutations and scalings a imed at placing large entries on the diagonal in the context of preconditio ning for general sparse matrices. The permutations and scalings are those d eveloped by Olschowka and Neumaier [Linear Algebra Appl., 240 (1996), pp. 1 31-151] and by Duff and Koster [SIAM J. Matrix Anal. Appl., 20 (1999), pp. 889-901; Tech report Ral-Tr-99-030, Rutherford Appleton Laboratory, Chilton , UK, 1999]. We target highly indefinite, nonsymmetric problems that cause difficulties for preconditioned iterative solvers. Our numerical experiment s indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing.