Linear and strong convergence of algorithms involving averaged nonexpansive operators

We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong convergence results for quasicyclic, cyclic, and random iterations. New convergence results on the Borwein–Tam method (BTM) and on the cyclically anchored Douglas–Rachford algorithm (CADRA) are also presented. Finally, we provide a numerical comparison of BTM, CADRA and the classical method of cyclic projections for solving convex feasibility problems.