Accelerating the shift-splitting iteration algorithm

摘要

The dazzling property of shift-splitting iteration method is unconditional convergence for any parameters and Anderson mixing as a simple and classic method can greatly speed up convergence of fix point iterations. Inheriting the merits of them, we propose an accelerated preconditioning shift-splitting algorithm for generalized saddle point problems. Then, we verify its unconditional convergence. Besides, we discuss the spectrum distribution of iteration matrix and then provide the relationship of optimal parameters involved. Finally, numerical experiments underline its superiority both as a solver and preconditioner.