Linear and strong convergence of algorithms involving averaged\n nonexpansive operators

Abstract

We introduce regularity notions for averaged nonexpansive operators. Combined\nwith regularity notions of their fixed point sets, we obtain linear and strong\nconvergence results for quasicyclic, cyclic, and random iterations. New\nconvergence results on the Borwein-Tam method (BTM) and on the cylically\nanchored Douglas-Rachford algorithm (CADRA) are also presented. Finally, we\nprovide a numerical comparison of BTM, CADRA and the classical method of cyclic\nprojections for solving convex feasibility problems.\n