Two Matrix Splitting Iteration Methods For The Discrete Dynamic Complex Linear Systems

Based on the ideas of lopsided preconditioned modified Hermitian and skewHermitian splitting(LPMHSS)method as well as the complex matrix and skewHermitian splitting(CSS)method,the Lopsided Hermitian and complex splitting(LHCS)method is proposed in this paper for solving a class of complex symmetric indefinite linear systems rising from the n-degree-of freedom(n-DOF)discrete systems.The convergence properties of the LHCS iteration method are obtained.Under a loose restriction on parameter ,we also show the produced iterative sequence of the LHCS iteration method is convergent to the unique solution for any initial guess.Furthermore,an upper bound for the spectral radius of the LHCS iteration matrix is derived.By minimizing the above upper bound,a choice of the quasi-optimal parameter *is obtained.Moreover,we also present a block PSS method to solve a high frequency discrete dynamic n-DOF linear systems and study its convergence.Numerical experiments are reported to verify the efficiency of the LHCS method and the BPSS method.