Mixed Constraint Preconditioners for the iterative solution of FE coupled consolidation equations
Journal of Computational Physics
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
An alternating preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
Eigenvalue Estimates for Preconditioned Nonsymmetric Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
On generalized parameterized inexact Uzawa method for a block two-by-two linear system
Journal of Computational and Applied Mathematics
Hi-index | 0.01 |
The problem of finding good preconditioners for the numerical solution of an important class of indefinite linear systems is considered. These systems are of a regularized saddle point structure $[\begin{smallmatrix} A &\quad B^T \\ B &\quad -C \end{smallmatrix}] [\begin{smallmatrix} x \\ y \end{smallmatrix}] = [\begin{smallmatrix} c \\ d \end{smallmatrix}], $ where $A\in\mathbb R ^{n\times n}$, $C\in\mathbb R ^{m\times m}$ are symmetric and $B\in\mathbb R ^{m\times n}$. In [SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1300-1317], Keller, Gould, and Wathen analyze the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of $C$ being zero. We shall extend this idea by allowing the (2, 2) block to be symmetric and positive semidefinite. Results concerning the spectrum and form of the eigenvectors are presented, as are numerical results to validate our conclusions.