On parameter acceleration methods for saddle point problems

For solving saddle point problems, parameter acceleration methods which include Uzawa-type methods are investigated by many researchers in the literature. In this paper, we introduce the inexact Uzawa method with another parameter acceleration, that is, the so-called momentum acceleration method for solving saddle point problems. We discuss the convergence conditions of the inexact Uzawa iteration with momentum acceleration and give the optimal momentum factors which minimize the spectral radii of the associated iteration matrices. Numerical results demonstrate the effectiveness of the inexact Uzawa method with momentum acceleration and the mixed parameter acceleration methods for solving saddle point problems.