A new two-step method with identical coefficient matrices for complex symmetric linear systems

Abstract

A new two-step iteration method is constructed to solve complex symmetric linear systems inspired by the CRI method, and we call it as the ICCRI method by using two linear subsystems with identical coefficient matrices in each iteration. We present the elaborate discussion of the spectral radius of the iteration matrix for the ICCRI method, and obtain the quasi-optimal parameter. Particularly, the spectral radius of the iteration matrix is no more than 0.5 when the quasi-optimal parameter is used for the ICCRI method. Moreover, to make comparison with the CRI method, we also give detailed analyses on the quasi-optimal parameter and the corresponding convergence factor of the CRI method, which are not proved in the original article. Some numerical experiments are implemented and the results show that the new ICCRI method is more efficient than the PMHSS and the CRI methods.