Over-Relaxation in Alternating Projections

Abstract: We improve upon the current bound on convergence rates of the Gauss-Seidel, Kaczmarz, and more generally projection methods where projections are visited in randomized order. The tighter bound reveals a practical approach to speed up convergence by over-relaxation -- a longstanding challenge that has been difficult to overcome for general problems with deterministic Succession of Over-Relaxations.