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Error Control in Polytope Computations

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  • S.M. Veres

    (University of Southampton)

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.

Suggested Citation

  • S.M. Veres, 2002. "Error Control in Polytope Computations," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 325-355, May.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:2:d:10.1023_a:1014835026141
    DOI: 10.1023/A:1014835026141
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    References listed on IDEAS

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    1. Norton, J.P. & Mo, S.H., 1990. "Parameter bounding for time-varying systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 527-534.
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