An alternating preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks
SIAM Journal on Matrix Analysis and Applications
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
Parameterized preconditioning for generalized saddle point problems arising from the Stokes equation
Journal of Computational and Applied Mathematics
Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks
Journal of Computational and Applied Mathematics
Indefinite block triangular preconditioner for symmetric saddle point problems
Calcolo: a quarterly on numerical analysis and theory of computation
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
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We study the eigenvalue bounds of block two-by-two nonsingular and symmetric indefinite matrices whose $(1,1)$ block is symmetric positive definite and Schur complement with respect to its $(2,2)$ block is symmetric indefinite. A constraint preconditioner for this matrix is constructed by simply replacing the $(1,1)$ block by a symmetric and positive definite approximation, and the spectral properties of the preconditioned matrix are discussed. Numerical results show that, for a suitably chosen $(1,1)$ block-matrix, this constraint preconditioner outperforms the block-diagonal and the block-tridiagonal ones in iteration step and computing time when they are used to accelerate the GMRES method for solving these block two-by-two symmetric positive indefinite linear systems. The new results extend the existing ones about block two-by-two matrices of symmetric negative semidefinite $(2,2)$ blocks to those of general symmetric $(2,2)$ blocks.