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

Wei-Hua Luo and Ting-Zhu Huang

Full-text: Open access

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 α 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

Permanent link to this document
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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