Generalized shift-splitting iteration method for a class of two-by-two linear systems

In this paper, we propose a generalized-shift splitting (GSS) iteration method for solving a broad class of two-by-two linear systems. The convergence theory of the GSS iteration method is established and the spectral properties of the corresponding preconditioned matrix of some special choices for the parameter matrices are analyzed. In addition, the optimal choice of the iterative parameter is discussed. Numerical experiments are used to verify the validity of the theoretical results and the effectiveness of the new method.