1. On the eigenvalue distribution of preconditioned nonsymmetric saddle point matrices
- Author
-
Shuqian Shen, Wen-Di Bao, Ting-Zhu Huang, and Ling Jian
- Subjects
Algebra and Number Theory ,Preconditioner ,Applied Mathematics ,Block matrix ,Positive-definite matrix ,Computer Science::Numerical Analysis ,Mathematics::Numerical Analysis ,Combinatorics ,Matrix (mathematics) ,Product (mathematics) ,Conjugate gradient method ,Saddle point ,Applied mathematics ,Eigenvalues and eigenvectors ,Mathematics - Abstract
SUMMARY In this paper, we derive bounds for the complex eigenvalues of a nonsymmetric saddle point matrix with a symmetric positive semidefinite (2,2) block, that extend the corresponding previous bounds obtained by Bergamaschi. For the nonsymmetric saddle point problem, we propose a block diagonal preconditioner for the conjugate gradient method in a nonstandard inner product. Numerical experiments are also included to test the performance of the presented preconditioner. Copyright © 2013 John Wiley & Sons, Ltd.
- Published
- 2013