## 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

#### Abstract

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 $n$, 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 $\alpha \to 0$. 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.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 489295, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807324

Digital Object Identifier
doi:10.1155/2013/489295

Mathematical Reviews number (MathSciNet)
MR3045419

Zentralblatt MATH identifier
1266.65048

#### Citation

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

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