Algorithms for Polyhedral Approximation of Multidimensional Ellipsoids

Abstract

We present efficient and simple algorithms for the approximation of a d-dimensional ellipsoid by polytopes of a prescribed size which are either contained in or contain the ellipsoid. The polytopes provided by our algorithms have a high degree of regularity, which enables us to construct their j-skeletons, j=0,…,d−1, efficiently. The rate of approximation, as measured by the symmetric distance and up to a constant, is best possible by any algorithm.