A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems

We propose a variant of PMHSS iteration method for solving and preconditioning a class of complex symmetric indefinite linear systems. The unconditional convergence theory of this iteration method is proved, and the choice of quasi-optimal parameter is also discussed. The explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrix are derived. In addition, theoretical analyses show that all eigenvalues are linearly distributed in the unit circle under suitable conditions. Numerical experiments are reported to illustrate the effectiveness and robustness of the proposed method.