Modified HSS iteration methods for a class of non-Hermitian positive-definite linear systems

We consider the numerical solution of a class of non-Hermitian positive-definite linear systems by the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method. We show that the MHSS iteration method converges unconditionally even when the real and the imaginary parts of the coefficient matrix are nonsymmetric and positive semidefinite and, at least, one of them is positive definite. At each step the MHSS iteration method requires to solve two linear sub-systems with real nonsymmetric positive definite coefficient matrices. We propose to use inner iteration methods to compute approximate solutions of these linear sub-systems. We illustrate the performance of the MHSS method and its inexact variant by two numerical examples.