Fast parameterized inexact Uzawa method for complex symmetric linear systems

In previous years, Bai and Wang presented a class of parameterized inexact Uzawa (PIU) methods for solving the generalized saddle point problems. In this paper, we consider the same method for iteratively solving the complex symmetric linear systems. Our main contribution is accelerating the convergence of the parameterized inexact Uzawa method by correction technique. First, the corrected model for the PIU method is established and the corrected PIU method is presented. Then we study the convergence property of the corrected PIU method. In fact, the corrected PIU method can converge faster than some Uzawa-type and HSS-like methods. Finally, numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the new method.