Generalized Accelerated Hermitian and Skew-Hermitian Splitting Methods for Saddle-Point Problems

Abstract

We generalize the accelerated Hermitian and skew-Hermitian splitting(AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solution of the saddle-point problem. Numerical experiments are used to further examine the effectiveness and robustness of iterations.