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A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems

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  • Wei-Hua Luo
  • Ting-Zhu Huang

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 , 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.

Suggested Citation

  • Wei-Hua Luo & Ting-Zhu Huang, 2013. "A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, April.
    • Handle: RePEc:hin:jnljam:489295
    DOI: 10.1155/2013/489295
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