On the approximation properties of nonsmooth convex disks (Q1608251)

The author examines the accuracy of approximation of two-dimensional convex compact bodies by polygons. The well-known upper bounds on approximation accuracy are determined by \(\sim\;c/n^2\), where \(n\) is the number of vertices of the polygon. The goal of this work is to obtain a constructive upper bound on theaccuracy for nonsmooth bodies permitting a higher convergence rate then \(c/n^2\). An algorithm is constructed, for which a stronger bound is obtained for nonsmooth bodies.