Umbrellas and polytopal approximation of the Euclidean ball

Yehoram Gordon; Shlomo Reisner; Carsten Schütt

doi:10.1006/jath.1996.3065

Umbrellas and polytopal approximation of the Euclidean ball

Yehoram Gordon, Shlomo Reisner, Carsten Schütt

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

Abstract

There are two positive, absolute constants c₁ and c₂ so that the volume of the difference set of the d-dimensional Euclidean ball B^d₂ and an inscribed polytope with n vertices is larger than c₁ d vol _d(B^d₂) n^-2/(d-1) for n ≥ (c₂ d)^(d-1)/2.

Original language	English
Pages (from-to)	9-22
Number of pages	14
Journal	Journal of Approximation Theory
Volume	90
Issue number	1
DOIs	https://doi.org/10.1006/jath.1996.3065
State	Published - Jul 1997
Externally published	Yes

Bibliographical note

Funding Information:
* Yehoram Gordon was partially supported by the Fund for the Promotion of research at the Technion, and the France-Israel Arc en Ciel program. -Shlomo Reisner was supported by the France-Israel Arc en Ciel program and NSF Grant DMS-9626749. Carsten Schutt has been supported by NSF Grant DMS-9301506.

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1006/jath.1996.3065

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author = "Yehoram Gordon and Shlomo Reisner and Carsten Sch{\"u}tt",

note = "Funding Information: * Yehoram Gordon was partially supported by the Fund for the Promotion of research at the Technion, and the France-Israel Arc en Ciel program. -Shlomo Reisner was supported by the France-Israel Arc en Ciel program and NSF Grant DMS-9626749. Carsten Schutt has been supported by NSF Grant DMS-9301506.",

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AU - Schütt, Carsten

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N2 - There are two positive, absolute constants c1 and c2 so that the volume of the difference set of the d-dimensional Euclidean ball Bd2 and an inscribed polytope with n vertices is larger than c1 d vol d(Bd2) n-2/(d-1) for n ≥ (c2 d)(d-1)/2.

AB - There are two positive, absolute constants c1 and c2 so that the volume of the difference set of the d-dimensional Euclidean ball Bd2 and an inscribed polytope with n vertices is larger than c1 d vol d(Bd2) n-2/(d-1) for n ≥ (c2 d)(d-1)/2.

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Umbrellas and polytopal approximation of the Euclidean ball

Abstract

Bibliographical note

ASJC Scopus subject areas

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