<div class="csl-bib-body">
<div class="csl-entry">Besau, F. G., & Hoehner, S. (2024, August 15). <i>The intrinsic volume metric and new upper bounds for optimal polytopal approximation</i> [Conference Presentation]. Bernoulli-ims 11th World Congress in Probability and Statistics, Bochum, Germany. http://hdl.handle.net/20.500.12708/209756</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/209756
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dc.description.abstract
We introduce a new notion of metric for the class of convex bodies in d
-dimensional Euclidean space, measuring distance based on the intrinsic volume difference (or quermassintegral difference). This novel metric serves as a basis for establishing improved upper bounds for the asymptotic optimal approximation of the Euclidean unit ball by a polytope in general position.
Our results demonstrate an improvement by a factor of the dimension when compared to classical results on the asymptotic approximation of the intrinsic volume difference with polytopes restricted to the domain of the ball.
In our proof, we rely on a probabilistic construction to bound the asymptotic optimal polytope by random polytopes and utilize integral formulas by Blaschke--Petkantschin and Chern.
en
dc.language.iso
en
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dc.subject
approximation
en
dc.subject
convex body
en
dc.subject
intrinsic volume
en
dc.subject
metric
en
dc.subject
polytope
en
dc.subject
quermassintegral
en
dc.title
The intrinsic volume metric and new upper bounds for optimal polytopal approximation
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Longwood University, United States of America (the)
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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tuw.author.orcid
0000-0002-6596-6127
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tuw.author.orcid
0000-0003-4084-4550
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tuw.event.name
Bernoulli-ims 11th World Congress in Probability and Statistics
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tuw.event.startdate
12-08-2024
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tuw.event.enddate
16-08-2024
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tuw.event.online
Hybrid
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tuw.event.type
Event for scientific audience
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tuw.event.place
Bochum
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tuw.event.country
DE
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tuw.event.presenter
Besau, Florian Georg
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference paper not in proceedings
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
