Matrix analysis
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
A Primal-Based Penalty Preconditioner for Elliptic Saddle Point Systems
SIAM Journal on Numerical Analysis
Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems
SIAM Journal on Matrix Analysis and Applications
Constraint-Style Preconditioners for Regularized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
On nonsymmetric saddle point matrices that allow conjugate gradient iterations
Numerische Mathematik
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A Generalization of the Hermitian and Skew-Hermitian Splitting Iteration
SIAM Journal on Matrix Analysis and Applications
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We present a valid lower bound for the real eigenvalues of a nonsymmetric saddle point matrix even if its $(2,2)$ block is singular. This bound, together with bounds introduced by Benzi and Simoncini in [Numer. Math., 103 (2006), pp. 173-196], is applied for the analysis of symmetric indefinite preconditioners and primal-based penalty preconditioners. Eigenvalue estimates for the Hermitian and skew-Hermitian splitting preconditioned saddle point matrices are also derived. The model problem of Stokes equations is used to illustrate the presented theoretical results.