The Surface Area Deviation of the Euclidean Ball and a Polytope

Steven D. Hoehner; Carsten Schütt; Elisabeth M. Werner

doi:10.1007/s10959-016-0701-9

The Surface Area Deviation of the Euclidean Ball and a Polytope

Steven D. Hoehner
, Carsten Schütt
, Elisabeth M. Werner

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the symmetric surface area deviation.

Original language	English (US)
Pages (from-to)	244-267
Number of pages	24
Journal	Journal of Theoretical Probability
Volume	31
Issue number	1
DOIs	https://doi.org/10.1007/s10959-016-0701-9
State	Published - Mar 1 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Approximation
Polytopes
Surface deviation

Publisher link

10.1007/s10959-016-0701-9

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abstract = "While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the symmetric surface area deviation.",

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AU - Schütt, Carsten

AU - Werner, Elisabeth M.

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N2 - While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the symmetric surface area deviation.

AB - While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the symmetric surface area deviation.

KW - Approximation

KW - Polytopes

KW - Surface deviation

UR - https://www.scopus.com/pages/publications/84978153863

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The Surface Area Deviation of the Euclidean Ball and a Polytope

Abstract

Bibliographical note

Keywords

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