Journal ArticleDOI
Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems
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TLDR
A class of preconditioned Hermitian/skew-Hermitian splitting iteration methods is established, showing that the new method converges unconditionally to the unique solution of the linear system.Abstract:
For the positive semidefinite system of linear equations of a block two-by-two structure, by making use of the Hermitian/skew-Hermitian splitting iteration technique we establish a class of preconditioned Hermitian/skew-Hermitian splitting iteration methods. Theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly. Numerical examples further confirm the correctness of the theory and the effectiveness of the method.read more
Citations
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Hermitian and Skew-Hermitian splitting methods for non-Hermitian positive definite linear systems.
TL;DR: An upper bound of the contraction factor of the HSS iteration is derived which is dependent solely on the spectrum of the Hermitian part and is independent of the eigenvectors of the matrices involved.
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
On generalized successive overrelaxation methods for augmented linear systems
TL;DR: A generalized SOR (GSOR) method is presented to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation, matrix relaxation and inexact iteration.
Journal ArticleDOI
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
TL;DR: A new splitting is introduced, called positive-definite and skew-Hermitian splitting (PSS), and a class of PSS methods similar to the HSS and NSS method for iteratively solving the positive- definite systems of linear equations are established.
Journal ArticleDOI
Modulus‐based matrix splitting iteration methods for linear complementarity problems
TL;DR: Numerical results show that the modulus-based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency.
References
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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.
Book
Mixed and Hybrid Finite Element Methods
Franco Brezzi,Michel Fortin +1 more
TL;DR: Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.
Book
Iterative Methods for Solving Linear Systems
TL;DR: This paper presents a brief overview of the State of the Art Notation Review of Relevant Linear Algebra and some of the algorithms used in this review, as well as some basic ideas of Domain Decomposition Methods.
Book
Augmented Lagrangian methods : applications to the numerical solution of boundary-value problems
M. Fortin,Roland Glowinski +1 more
TL;DR: In this article, the authors present the principles of the augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.
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