A preconditioned SSOR iteration method for solving complex symmetric system of linear equations

Abstract

We present a preconditioned version of the symmetric successive overrelaxation (SSOR) iteration method for a class of complex symmetric linear systems. The convergence results of the proposed method are established and conditions under which the spectral radius of the iteration matrix of the method is smaller than that of the SSOR method are analyzed. Numerical experiments illustrate the theoretical results and depict the efficiency of the new iteration method.

Two new effective iteration methods for nonlinear systems with complex symmetric Jacobian matrices

“…Some algorithms, such as preconditioned modified HSS (PMHSS) method (Bai et al , 2011 and single step HSS (SHSS) method (Li and Wu 2015), were proposed later to improve the HSS method. Because of the efficiency of these HSS-based methods, many scholars have done a lot of research in recent years, see Xiao and Wang (2018); Huang et al (2018); Siahkolaei and Salkuyeh (2019); Zhang et al (2019); Wang et al (2017Wang et al ( , 2018. By applying these methods as inner iterations of Newton methods, the corresponding Newton-HSS type methods can be obtained, such as Newton-HSS method (Bai and Guo 2010) and Newton-MHSS method (Yang and Wu 2012), which have been used and studied widely.…”