The circumcentered-reflection method achieves better rates than alternating projections

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