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

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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.

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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.

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