Approximating optimal parameters for generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) method.

Generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) method is a numerical method for obtaining the solution of linear systems with complex symmetric semi-positive definite coefficient matrix. This method relates to the two relaxed parameters that should be chosen properly and is a hard task mathematically. In this study, based on the work in [J. Comput. Appl. Math. 255, 142–149 (2014)] that investigates the optimum parameter for the HSS method, we expand the results of this paper for computing optimum parameters for GPHSS method. We will show that these parameters are obtained by minimizing a function of two variables. Finally in the numerical section, we study some test problems to support the theoretical discussion. [ABSTRACT FROM AUTHOR]