Modified two-step scale-splitting iteration method for solving complex symmetric linear systems

For the large sparse complex symmetric linear systems, based on the combination method of real part and imaginary part method established by Wang et al. (J Comput Appl Math 325:188–197, 2017) and the double-step scale splitting one derived by Zheng et al. (Appl Math Lett 73:91–97, 2017), we construct a modified two-step scale-splitting (MTSS) iteration method in this paper. The convergence properties of the MTSS iteration method and its quasi-optimal parameters which minimizes the upper bound for the spectral radius of the proposed method are presented. Meanwhile, we derive the inexact variant of the MTSS iteration method. On this basis, we also introduce a minimum residual MTSS iteration method and its inexact version and give their convergence analyses. Numerical results on complex symmetric linear systems support that the proposed methods are more efficient and robust than some other commonly used ones.

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