convergence properties of hermitian and skew hermitian splitting methods

Convergence Properties of Hermitian and Skew Hermitian Splitting Methods

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices

For the non-Hermitian and positive semidefinite systems of linear equations, we derive sufficient and necessary conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. These result is specifically applied to linear systems of block tridiagonal form to obtain convergence conditions for the corresponding block varia...

On Modified Hermitian and Skew - Hermitian Splitting

Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems

Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skewHermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for nonHermitian positive-definite linear systems, Numer. Lin. Alg. Appl., 14 (2007): 217-235]. Key-Word...

A Generalization of the Hermitian and Skew-hermitian Splitting Iteration∗

This paper is concerned with a generalization of the Hermitian and skew-Hermitian (HSS) splitting iteration for solving positive definite, non-Hermitian linear systems. It is shown that the new scheme can outperform the standard HSS method in some situations and can be used as an effective preconditioner for certain linear systems in saddle point form. Numerical experiments using discretization...

Two-parameter generalized Hermitian and skew-Hermitian splitting iteration method

It is known that the Hermitian and skew-Hermitian splitting (HSS) iteration method is an efficient solver for non-Hermitian positive definite linear system of equations. In [M. Benzi, SIAM J. Matrix Anal. Appl. 31 (2009) 360–374] Benzi proposed a generalization of the HSS (GHSS) iteration method. In this paper, we present a two-parameter version of the GHSS (TGHSS) method and investigate its co...