A SIMPLE AUGMENTED JACOBI METHOD FOR HERMITIAN AND SKEW-HERMITIAN MATRICES

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.

Optimal Parameter in Hermitian and Skew-Hermitian Splitting Method for Certain Two-by-Two Block Matrices

The optimal parameter of the Hermitian/skew-Hermitian splitting (HSS) iteration method for a real 2-by-2 linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain 2-by-2 block matrices, and to estimate the optimal parameters of the HSS iteration method for linear systems with n-by-n real coefficient matrices. Numerical examples ...

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...

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...

On Modified Hermitian and Skew - Hermitian Splitting