AQTTTS-based iteration methods for weakly nonlinear systems with diagonal-plus-Toeplitz structure

In this paper, motivated by the quasi-Toeplitz trigonometric transform splitting (QTTTS) method, we propose the acceleration of the QTTTS (AQTTTS) iteration method for the linear system with diagonal-plus-Toeplitz structure. Then, using the AQTTTS method as the inner iteration, we establish the Picard-AQTTTS and nonlinear AQTTTS-like methods for solving the weakly nonlinear systems with diagonal-plus-Toeplitz structure. Moreover, we give the analysis of the convergence properties of the new methods under suitable conditions. Finally, numerical results show that these new methods are effective.