A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-21
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Luo, Wei-Hua& Huang, Ting-Zhu. 2013. A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-475662
Modern Language Association (MLA)
Luo, Wei-Hua& Huang, Ting-Zhu. A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems. Journal of Applied Mathematics No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-475662
American Medical Association (AMA)
Luo, Wei-Hua& Huang, Ting-Zhu. A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-475662
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-475662