Two variants of the PMHSS iteration method for a class of complex symmetric indefinite linear systems

For a class of complex symmetric indefinite linear systems, we present two variants of the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method. One is a generalization of the PMHSS iteration method and the other is a generalization of the lopsided PMHSS iteration method. We study the convergence properties of these two variants by analyzing the upper bounds of spectral radiuses of the corresponding iteration matrices and compare these upper bounds. Numerical examples are illustrated to show the effectiveness of the proposed iteration methods.