Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Matrix computations (3rd ed.)
An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Solution of Augmented Systems Arising in Interior Methods
SIAM Journal on Optimization
Block preconditioning for saddle point systems with indefinite (1, 1) block
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability
SIAM Journal on Scientific Computing
Constraint Preconditioners for Symmetric Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
Direct solution of linear systems of size 109 arising in optimization with interior point methods
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
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We provide eigenvalue intervals for symmetric saddle point and regularized saddle point matrices in the case where the (1,1) block may be indefinite. These generalize known results for the definite (1,1) case. We also study the spectral properties of the equivalent augmented formulation, which is an alternative to explicitly dealing with the indefinite (1,1) block. Such an analysis may be used to assess the convergence of suitable Krylov subspace methods. We conclude with spectral analyses of the effects of common block-diagonal preconditioners.