Complex-extrapolated MHSS iteration method for singular complex symmetric linear systems

In this paper, by extrapolating the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method with a complex relaxation parameter, a complex-extrapolated MHSS (CMHSS) iteration method is present for solving a class of complex singular symmetric of linear equations. We study the semi-convergence properties of the CMHSS iteration method and the extent of the optimal iterative parameters. Furthermore, the convergence conditions also hold for solving nonsingular complex systems. Numerical experiments are given to verify the effectiveness of the CMHSS iteration method for solving both singular and nonsingular complex symmetric systems.

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