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We study the convergence rate of the Circumcentered-Reflection Method (CRM)for solving the convex feasibility problem and compare it with the Method ofAlternating Projections (MAP). Under an error bound assumption, we prove thatboth methods converge linearly, with asymptotic constants depending on aparameter of the error bound, and that the one derived for CRM is strictlybetter than the one for MAP. Next, we analyze two classes of fairly genericexamples. In the first one, the angle between the convex sets approaches zeronear the intersection, so that the MAP sequence converges sublinearly, but CRMstill enjoys linear convergence. In the second class of examples, the anglebetween the sets does not vanish and MAP exhibits its standard behavior, i.e.,it converges linearly, yet, perhaps surprisingly, CRM attains superlinearconvergence.

The circumcentered-reflection method achieves better rates than alternating projections