Accelerated double-step scale splitting iteration method for solving a class of complex symmetric linear systems

Abstract

In this paper, we introduce and study an accelerated double-step scale splitting (ADSS) iteration method for solving complex linear systems. The convergence of the ADSS iteration method is determined under suitable conditions. Also each iteration of ADSS method requires the solution of two linear systems that their coefficient matrices are real symmetric positive definite. We analytically prove that the ADSS iteration method is faster than the DSS iteration method. Moreover, to increase the convergence rate of this method, we minimize the upper bound of the spectral radius of iteration matrix. Finally, some test problems will be given and simulation results will be reported to support the theoretical results.