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Abstract By utilizing the successive-overrelaxation (SOR) acceleration technique for the generalized version of the double-step scale (DSS) iteration method, we construct the generalized DSS-SOR (GDSSOR) iteration method for solving a class of complex symmetric linear systems. The convergence theory of the GDSSOR iteration method is established and its optimal parameters are investigated. Meanwhile, a practical way to choose iteration parameters for the GDSSOR iteration method is developed. Inexact version of the GDSSOR iteration (IGDSSOR) method and its convergence properties are also presented. Numerical experiments illustrate that both GDSSOR and IGDSSOR iteration methods are feasible and effective for solving the complex symmetric linear systems, and perform better than some other commonly used iteration methods. [ABSTRACT FROM AUTHOR]

For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSS) preconditioner as well as the MGSS iteration method is derived in this paper, which generalize the modified shift-splitting (MSS) preconditioner and the MSS iteration method newly developed by Huang and Su (J. Comput. Appl. Math. 317:535-546, 2017), respectively. The convergent and semi-convergent analyses of the MGSS iteration method are presented, and we prove that this method is unconditionally convergent and semi-convergent. Meanwhile, some spectral properties of the preconditioned matrix are carefully analyzed. Numerical results demonstrate the robustness and effectiveness of the MGSS preconditioner and the MGSS iteration method and also illustrate that the MGSS iteration method outperforms the generalized shift-splitting (GSS) and the generalized modified shift-splitting (GMSS) iteration methods, and the MGSS preconditioner is superior to the shift-splitting (SS), GSS, modified SS (M-SS), GMSS and MSS preconditioners for the generalized minimal residual (GMRES) method for solving the nonsymmetric saddle point problems. [ABSTRACT FROM AUTHOR]