A class of constraint preconditioners for nonsymmetric saddle point matrices. (English) Zbl 1148.65031
Summary: We consider the use of a class of constraint preconditioners for the application of the Krylov subspace iterative method to the solution of large nonsymmetric, indefinite linear systems. The eigensolution distribution of the preconditioned matrix is determined and the convergence behavior of a Krylov subspace method such as GMRES is described. The choices of the parameter matrices and the implementation of the preconditioning step are discussed. Numerical experiments are presented.
MSC:
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
preconditioner; saddle point matrix; minimal polynomial; Schilders’ factorization; Krylov subspace iterative method; GMRES; numerical experimentsReferences:
| [1] | Benzi, Acta Numerica., 14, 1 (2005) · Zbl 1115.65034 · doi:10.1017/S0962492904000212 |
| [2] | Cao, SIAM J. Matrix Anal. Appl., 24, 121 (2002) · Zbl 1018.65060 · doi:10.1137/S0895479801391424 |
| [3] | Dollar, H.S., Wathen, A.J.: Incomplete factorization constraint precondiotioners for saddle point matrices. Technical report, NA-04/01, Oxford University Computing Laboratory, Numerical Analysis Group, 2004 |
| [4] | Dollar, H.S., Gould, N.I., Wathen, A.J.: On implicit-factorization constraint precondiotioners. Technical report, RAL-TR-2004-036, Rutherford Appleton Laboratory Oxfordshire, England, 2004 · Zbl 1108.65040 |
| [5] | Elman, SIAM J. Sci. Comput., 20, 1299 (1999) · Zbl 0935.76057 · doi:10.1137/S1064827596312547 |
| [6] | Keller, SIAM J. Matrix Anal. Appl., 21, 1300 (2000) · Zbl 0960.65052 · doi:10.1137/S0895479899351805 |
| [7] | Murphy, SIAM J. Sci. Comput., 21, 1969 (2000) · Zbl 0959.65063 · doi:10.1137/S1064827599355153 |
| [8] | Gould, SIAM J. Sci. Comput., 23, 1376 (2001) · Zbl 0999.65050 · doi:10.1137/S1064827598345667 |
| [9] | Saad, Y.: Iterative methods for sparse linear systems. PWS Publishing Company, Boston, 1996 · Zbl 1031.65047 |
| [10] | Saad, SIAM J. Sci. Stat. Comput., 7, 856 (1986) · Zbl 0599.65018 · doi:10.1137/0907058 |
| [11] | Saad, SIAM J. Sci. Stat. Comput., 14, 461 (1993) · Zbl 0780.65022 · doi:10.1137/0914028 |
| [12] | Van de Vorst, H.A.: Iterative Krylov methods for large systems. Cambridge University Press, Cambridge, United Kingdom, 2003 · Zbl 1023.65027 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
