The University of Southampton
University of Southampton Institutional Repository

Error control in polytope computations

Error control in polytope computations
Error control in polytope computations
This paper presents solutions for numerical computation on convex hulls; computational algorithms that ensure logical consistency and accuracy are proposed. A complete numerical error analysis is presented. It is shown that a global error bound for vertex-facet adjacency does not exist under logically consistent procedures. To cope with practical requirements, vertex preconditioned polytope computations are introduced using point and hyperplane adjustments. A global bound on vertex-facet adjacency error is affected by the global bound on vertices; formulas are given for a conservative choice of global error bounds.
polytopes and polyhedra, computational geometry, numerical analysis, linear optimization
0022-3239
325-355
Veres, S.M.
909c60a0-56a3-4eb6-83e4-d52742ecd304
Veres, S.M.
909c60a0-56a3-4eb6-83e4-d52742ecd304

Veres, S.M. (2002) Error control in polytope computations. Journal of Optimization Theory and Applications, 113 (2), 325-355. (doi:10.1023/A:1014835026141).

Record type: Article

Abstract

This paper presents solutions for numerical computation on convex hulls; computational algorithms that ensure logical consistency and accuracy are proposed. A complete numerical error analysis is presented. It is shown that a global error bound for vertex-facet adjacency does not exist under logically consistent procedures. To cope with practical requirements, vertex preconditioned polytope computations are introduced using point and hyperplane adjustments. A global bound on vertex-facet adjacency error is affected by the global bound on vertices; formulas are given for a conservative choice of global error bounds.

Text
22270.pdf - Version of Record
Restricted to Repository staff only

More information

Published date: 2002
Keywords: polytopes and polyhedra, computational geometry, numerical analysis, linear optimization

Identifiers

Local EPrints ID: 22270
URI: http://eprints.soton.ac.uk/id/eprint/22270
ISSN: 0022-3239
PURE UUID: 235d7311-0301-48ab-91bd-d72170f964d9

Catalogue record

Date deposited: 21 Mar 2006
Last modified: 19 Jul 2019 19:11

Export record

Altmetrics

Contributors

Author: S.M. Veres

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×