The rate of convergence for the cyclic projections algorithm II: Norms of nonlinear operators

Abstract

The rate of convergence for the cyclic projections algorithm onto an intersection of finitely many closed convex sets in a Hilbert space is investigated. Recently we showed that this rate could be described in terms of the “angles” between the convex sets involved. Here we show that these angles may often be described in terms of the “norms” of certain nonlinear operators, and hence obtain an alternate way of computing this rate of convergence.