GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Any Nonincreasing Convergence Curve is Possible for GMRES
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Primal-dual interior-point methods
Primal-dual interior-point methods
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
SIAM Journal on Matrix Analysis and Applications
The Quadratic Eigenvalue Problem
SIAM Review
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Computational Optimization and Applications
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The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block (KKT) structure in which the (2,2) block (denoted by -C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems, SIAM J. Matrix Anal. Appl. 21 (2000), Keller, Gould and Wathen introduced the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of C being zero. We shall give results concerning the spectrum and form of the eigenvectors when a preconditioner of the form considered by Keller, Gould and Wathen is used but the system we wish to solve may have C 驴0. In particular, the results presented here indicate clustering of eigenvalues and, hence, faster convergence of Krylov subspace iterative methods when the entries of C are small; such a situations arise naturally in interior point methods for optimization and we present results for such problems which validate our conclusions.