Asymptotic approximation of smooth convexbodies by polytopes 1
نویسندگان
چکیده
We study asymptotic properties of the approximation of a suuciently smooth convex body K in R d by the convex hulls of n points in the boundary of K, for n ! 1. The deviation is measured by the Hausdorr distance. The asymptotic distribution of the vertices of best-approximating polytopes is determined. Further results involve prescribed densities for the vertices and describe the strength of approximation by either deterministic or random polytopes.
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