The rate of convergence for the cyclic projections algorithm I: Angles between convex sets

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. We study the rate of convergence for the cyclic projections algorithm. The notion of angle between convex sets is defined, which generalizes the angle between linear subspaces. The rate of convergence results are described in terms of these angles.