Lecture on Numerical Linear Algebra
- Lecture on Numerical Linear Algebra
- 20F, Seminar Room 1 (2006), National Institute of Informatics
- June 11th (Monday), 2-3pm
- Nearly Optimal Block Preconditioners for Saddle Point Linear Systems
Professor Zhong-Zhi Bai (Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences)
For the structured systems of linear equations arising from the Galerkin finite-element discretizations of the distributed control problems, we construct block-counter-diagonal and block-counter-tridiagonal preconditioning matrices to precondition the Krylov subspace methods such as GMRES.
We derive explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices.
Numerical implementations show that these structured preconditioners may lead to satisfactory experimental results of the preconditioned GMRES methods when the regularization parameter is suitably small.
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