Approximation of Smooth Convex Bodies by Random Circumscribed Polytopes
نویسنده
چکیده
Choose n independent random points on the boundary of a convex body K ⊂Rd . The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n→∞ are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best approximating polytopes.
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