On semi-convergence of the parameterized generalized MHSS method for singular complex linear systems

For solving a class of complex symmetric singular linear systems, we propose a parameterized generalized MHSS (PGMHSS) iteration method and investigate the semi-convergence conditions by analyzing the spectrum of the iteration matrix. Then we analyze the optimal iteration parameters that minimize the upper bound of the semi-convergence factor. Numerical experiments are used to test the feasibility and the effectiveness of the PGMHSS iteration method.