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On triangulations for computing fixed points

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Abstract

This paper introduces theoretical measures of efficiency for triangulations used in computing fixed points. The measures, for both regular triangulations ofR n and those with continuous refinement of grid size, are based on an average count of the number of simplices met by straight line segments. The computation of these measures is facilitated by a description of the facets as well as the vertices of a triangulation. We give a simple description of a modification of Eaves' and Saigal's K3 and compute the measures of efficiency of three regular triangulations ofR n and two triangulations of (0, 1] ×R n with continuous refinement of grid size, including the modified K3.

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Authors and Affiliations

  1. Cornell University, Ithaca, N.Y., USA

    Michael J. Todd

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  1. Michael J. Todd
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This research was supported by National Science Foundation Grant GK-42092.

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Todd, M.J. On triangulations for computing fixed points. Mathematical Programming 10, 322–346 (1976). https://doi.org/10.1007/BF01580679

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  • DOI: https://doi.org/10.1007/BF01580679

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