A parameterized splitting iteration method for complex symmetric linear systems

In this paper, we propose a parameterized splitting (PS) iteration method for solving complex symmetric linear systems. The convergence theory of the method is established and the spectral properties of the corresponding iteration matrix are analyzed. The explicit expression for the spectral radius of the iteration matrix is given. In addition, the optimal choice of the iteration parameter is discussed. It is shown that the eigenvalues of the preconditioned matrix are cluster at 1. Numerical experiments illustrate the theoretical results and also examine the numerical effectiveness of the new parameterized splitting iteration method served either as a preconditioner or as a solver.