Linear and strong convergence of algorithms involving averaged nonexpansive operators

Understand

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 cylically 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.