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For solving a class of complex symmetric linear system, we first transform the system into a block two-by-two real formulation and construct a symmetric block triangular splitting (SBTS) iteration method based on two splittings. Then, eigenvalues of iterative matrix are calculated, convergence conditions with relaxation parameter are derived, and two optimal parameters are obtained. Besides, we present the optimal convergence factor and test two numerical examples to confirm theoretical results and to verify the high performances of SBTS iteration method compared with two classical methods. [ABSTRACT FROM AUTHOR]

In this paper, a double-step scale splitting (DSS) iteration method is proposed to solve a class of complex symmetric of linear equation. Unconditional convergence result is established under appropriate restrictions. Two reciprocal optimal iteration parameters and the corresponding optimal convergence factor are also determined. Numerical experiments on a few model problems are used to verify the effectiveness of the DSS iteration method. [ABSTRACT FROM AUTHOR]

In this note, the block-diagonal preconditioner proposed and the block triangular proposed in Krendl et al. (2013) and Pearson and Wathen (2012), respectively, are further studied and optimized. Two improved preconditioners are proposed for solving a class of complex linear systems arising from optimal control with time-periodic parabolic equation. Theoretical analyses show that the eigenvalues of the improved block-diagonal and block triangular preconditioned matrices are located in [ − 1 , − 2 / 2 ) ∪ ( 2 / 2 , 1 ] and ( 1 / 2 , 1 ] , respectively. Numerical experiments illustrate the feasibility and effectiveness of these preconditioners for Krylov subspace methods. [ABSTRACT FROM AUTHOR]