Polyhedral approximations of strictly convex compacta

TL;DR

This paper studies polyhedral approximations of strictly convex compact sets in Euclidean spaces, providing optimal error bounds in the Hausdorff metric and introducing improved algorithms for convex hull approximation.

Contribution

It offers the best possible error estimates for polyhedral approximations and develops new algorithms for convex hull computation.

Findings

Optimal error bounds in Hausdorff metric for approximations

New estimates for algorithms computing convex hulls

Enhanced methods for polyhedral approximation of convex sets

Abstract

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls.