Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2013, Special Issue (2012), Article ID 489295, 6 pages.
A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems
By using Sherman-Morrison-Woodbury formula, we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. By analyzing the eigenvalues of the preconditioned matrix, we find that when α is big enough, it has an eigenvalue at 1 with multiplicity at least , and the remaining eigenvalues are all located in a unit circle centered at 1. Particularly, when the preconditioner is used in general saddle point problems, it guarantees eigenvalue at 1 with the same multiplicity, and the remaining eigenvalues will tend to 1 as the parameter . Consequently, this can lead to a good convergence when some GMRES iterative methods are used in Krylov subspace. Numerical results of Stokes problems and Oseen problems are presented to illustrate the behavior of the preconditioner.
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 489295, 6 pages.
First available in Project Euclid: 14 March 2014
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Luo, Wei-Hua; Huang, Ting-Zhu. A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems. J. Appl. Math. 2013, Special Issue (2012), Article ID 489295, 6 pages. doi:10.1155/2013/489295. https://projecteuclid.org/euclid.jam/1394807324