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

我们研究了解决凸性可行性问题的“中心反射法”（CRM）的收敛速度，并将其与“交替投影法”（MAP）进行了比较。在错误界限的假设下，我们证明了这两种方法都是线性收敛的，并且渐进常数取决于错误界限的参数，并且针对CRM推导的方法严格优于针对MAP的方法。接下来，我们分析两类相当通用的示例。在第一个中，凸集之间的角度在相交处接近零，因此MAP序列亚线性收敛，但CRM仍然享有线性收敛。在第二类示例中，集合之间的角度不消失，并且MAP表现出其标准行为，即，它线性收敛，但是，令人惊讶的是，CRM实现了超线性收敛。