1
2
3
4
5
Constraint Preconditioning for Indefinite Linear Systems
Reads0
Chats0
TLDR
The problem of finding good preconditioners for the numerical solution of indefinite linear systems is considered and special emphasis is put on preconditionsers that have a 2 × 2 block structure and that incorporate the (1,2 and (2,1) blocks of the original matrix.Abstract:
The problem of finding good preconditioners for the numerical solution of indefinite linear systems is considered. Special emphasis is put on preconditioners that have a 2 × 2 block structure and that incorporate the (1,2) and (2,1) blocks of the original matrix. Results concerning the spectrum and form of the eigenvectors of the preconditioned matrix and its minimum polynomial are given. The consequences of these results are considered for a variety of Krylov subspace methods. Numerical experiments validate these conclusions.read more
Citations
More filters
Book
Numerical Optimization
Jorge Nocedal,Stephen J. Wright +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Journal ArticleDOI
Numerical solution of saddle point problems
TL;DR: A large selection of solution methods for linear systems in saddle point form are presented, with an emphasis on iterative methods for large and sparse problems.
Book ChapterDOI
Knitro: An Integrated Package for Nonlinear Optimization
TL;DR: The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings, and it is effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming.
Journal ArticleDOI
A Preconditioner for Generalized Saddle Point Problems
Michele Benzi,Gene H. Golub +1 more
TL;DR: A preconditioning strategy based on the symmetric\slash skew-symmetric splitting of the coefficient matrix is proposed, and some useful properties of the preconditionsed matrix are established.
Journal ArticleDOI
Interior point methods 25 years later
TL;DR: Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization as mentioned in this paper, including low-degree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations which depends very little, if at all, on the problem dimension.
References
More filters
Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Journal ArticleDOI
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Journal ArticleDOI
The Symmetric Eigenvalue Problem.
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.