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2013 A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems
Wei-Hua Luo, Ting-Zhu Huang
J. Appl. Math. 2013(SI03): 1-6 (2013). DOI: 10.1155/2013/489295


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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Wei-Hua Luo. Ting-Zhu Huang. "A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems." J. Appl. Math. 2013 (SI03) 1 - 6, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.65048
MathSciNet: MR3045419
Digital Object Identifier: 10.1155/2013/489295

Rights: Copyright © 2013 Hindawi


Vol.2013 • No. SI03 • 2013
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