An equidistant parameterized Gauss–Seidel iteration method for a class of block two-by-two linear systems

Abstract

In this work, an equidistant parameterized Gauss–Seidel (EPGS) iteration method based on a scale-splitting formulation of matrix is proposed for solving a class of block two-by-two real linear systems. Then, we investigate the convergence properties of this method and derive the optimal value of a relaxation parameter as well as the corresponding convergence factor. Furthermore, the spectral properties of EPGS-preconditioner are studied when the EPGS splitting matrix serves as a preconditioner to improve Krylov subspace methods. Finally, some numerical experiments are performed and discussed to demonstrate the performance of our method, and numerical results show that this novel method outperforms than classical iteration methods including PMHSS, E-HS, and GSOR.