Constructing a polytope to approximate a convex body期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Constructing a polytope to approximate a convex body

Authors:	Yehoram Gordon Mathieu Meyer Shlomo Reisner

Affiliation:	(1) Department of Mathematics, Technion I.I.T., 32000 Haifa, Israel;(2) Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, 2, rue de la Butte Verte, 93166 Noisy-le-Grand Cedex, France;(3) Department of Mathematics and School of Education — Oranim, University of Haifa, 31905 Haifa, Israel

Abstract:	We develop an algorithm to construct a convex polytopeP withn vertices, contained in an arbitrary convex bodyK inR^d, so that the ratio of the volumes \|K/P\|/\|K\| is dominated byc ·. d/n^2/(d–1).Supported in part by the fund for the promotion of research in the Technion

Keywords:	52A20 52A25
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