Double-step scale splitting real-valued iteration method for a class of complex symmetric linear systems

摘要

A double-step scale splitting (DSS) real-valued iteration method is constructed to solve an block two-by-two real linear system, which is deduced equivalently from a complex symmetric linear system. The convergence analysis for this DSS real-valued iteration method is presented under suitable conditions, and the upper bound of its spectral radius is proved to be smaller than that of the PMHSS real-valued iteration method. Furthermore, an improved DSS (IDSS) real-valued iteration method is derived by respectively adding two matrices to the coefficient matrices of the DSS iterative scheme, and the corresponding convergence analysis is also discussed. Finally, some numerical examples are given to illustrate the effectiveness and robustness of the proposed methods.