Nonlinear Schwarz iterations with reduced rank extrapolation

Extrapolation methods can be a very effective technique used for accelerating the convergence of vector sequences. In this paper, these methods are used to accelerate the convergence of Schwarz iterative methods for nonlinear problems. A new implementation of the reduced-rank-extrapolation (RRE) method is introduced. Some convergence analysis is presented, and it is shown numerically that certain extrapolation methods can indeed be very effective in accelerating the convergence of Schwarz methods.