Error Control in Polytope Computations

S.M. Veres
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S.M. Veres: University of Southampton

Journal of Optimization Theory and Applications, 2002, vol. 113, issue 2, No 7, 325-355

Abstract: 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.

Keywords: Polytopes and polyhedra; computational geometry; numerical analysis; linear optimization (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1014835026141

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