Linear and strong convergence of algorithms involving averaged nonexpansive operators

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