On convergence and semi-convergence of SSOR-like methods for augmented linear systems

In this paper, we analyze the convergence and semi-convergence of a class of SSOR-like methods with four real functions for augmented systems. The class takes most existed SSOR-like methods as its special cases. For nonsingular systems, we obtain the minimum of convergence factors of all the SSOR-like methods in the class, and study when it can be reached by the convergence factors of methods in the class. By considering the equivalence of methods, we show that most of the existed SSOR-like methods have the same minimum of convergence factors.