Modified CRI iteration methods for complex symmetric indefinite linear systems

This work investigates the iterative solution of complex symmetric linear systems with indefinite matrix term. Based on a technical equivalent reformulation of the original indefinite systems, an efficient stationary splitting iteration method is established by combining with its real and imaginary parts. In the view of the structure, the new method can be viewed as a modification of the combination method of the real and imaginary parts (CRI) in Wang 325:188–197, which is originally designed for solving complex symmetric linear systems with positive semi-definite coefficient matrices. Despite that it is devoted to more difficult indefinite problems, the new method keeps the merits of unconditional convergence and parameter free implementation of the original method. Moreover, Chebyshev polynomial acceleration is considered to further improve the convergence rate of the new method. Numerical experiments on a set of model problems are tested to illustrate the efficiency of the proposed methods compared with some existing ones.