Acceleration schemes for the method of alternating projections

摘要

In this paper, we develop and analyze schemes for accelerating the convergence of the alternating projections method for finding the projection of a point onto the intersection of a finite number of subspaces of a Hilbert space. A special method for the case of two subspaces is developed, and two general schemes are determined for the case of an arbitrary number of subspaces. Proofs of convergence and acceleration are given for each method. Finally, techniques for constructing test problems are outlined and the results of computational experiments are reported.