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
325-355
Veres, S.M.
909c60a0-56a3-4eb6-83e4-d52742ecd304
2002
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), .
(doi:10.1023/A:1014835026141).
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.
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Published date: 2002
Keywords:
polytopes and polyhedra, computational geometry, numerical analysis, linear optimization
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Local EPrints ID: 22270
URI: http://eprints.soton.ac.uk/id/eprint/22270
ISSN: 0022-3239
PURE UUID: 235d7311-0301-48ab-91bd-d72170f964d9
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Date deposited: 21 Mar 2006
Last modified: 15 Mar 2024 06:36
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Author:
S.M. Veres
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