Standard preconditioners, like incomplete factorizations, perform well when the coefficient 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. The permutations and scalings are those developed by Olschowka and Neumaier [Linear Algebra Appl., 240 (1996), pp. 131-151] 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 experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing.
Preconditioning highly indefinite and nonsymmetric matrices
Benzi, M.;
2001
Abstract
Standard preconditioners, like incomplete factorizations, perform well when the coefficient 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. The permutations and scalings are those developed by Olschowka and Neumaier [Linear Algebra Appl., 240 (1996), pp. 131-151] 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 experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
