Efficient block splitting iteration methods for solving a class of complex symmetric linear systems

Abstract

In this paper, we first propose a new block splitting (NBS) iteration method for solving the large sparse complex symmetric linear systems. The NBS iteration method avoids complex arithmetic compared with the combination method of real part and imaginary part (CRI) one established by Wang et al. (2017). The unconditional convergence and the quasi-optimal parameter of the NBS iteration method are given. Moreover, by further accelerating the NBS one with another parameter, we construct the parameterized BS (PBS) iteration method and establish its convergence theory. Also, the spectral properties of the PBS-preconditioned matrix are analyzed and the parameter selection strategy of the PBS iteration method is given. Numerical experiments are reported to illustrate the feasibility and effectiveness of the proposed methods.