Parameterized QHSS Iteration Method and Its Variants for Non-Hermitian Positive Definite Linear Systems of Strong Skew-Hermitian Parts

Based on the quasi-Hermitian and skew-Hermitian splitting (QHSS) iteration method proposed by Bai for solving the large sparse non-Hermitian positive definite linear systems of strong skew-Hermitian parts, this paper introduces a parameterized QHSS (PQHSS) iteration method. The PQHSS iteration is essentially a two-parameter iteration which covers the standard QHSS iteration and can further accelerate the iterative process. In addition, two practical variants, viz., inexact and extrapolated PQHSS iteration methods are established to further improve the computational efficiency. The convergence conditions for the iteration parameters of the three proposed methods are presented. Numerical results illustrate the effectiveness and robustness of the PQHSS iteration method and its variants when used as linear solvers, as well as the PQHSS preconditioner for Krylov subspace iteration methods.