On the approximation of a polytope by its dual L p - centroid bodies ∗
نویسندگان
چکیده
We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P ∈ R by its dual Lp-centroid bodies is independent of the geometry of P . In particular we show that if P has volume 1, lim p→∞ p log p „ |Z◦ p (P )| |P ◦| − 1 « = n. We provide an application to the approximation of polytopes by uniformly convex sets.
منابع مشابه
On the approximation of a polytope
We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P ∈ R by its dual Lp-centroid bodies is independent of the geometry of P . In particular we show that if P has volume 1, lim p→∞ p log p „ |Z◦ p (P )| |P ◦| − 1 « = n. We provide an application to the approximation of polytopes by uniformly convex sets.
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تاریخ انتشار 2011