Construction of polygonal interpolants: a maximum entropy approach

Authors

  • N. Sukumar

    Corresponding author
    1. Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, U.S.A.
    • Department of Civil and Environmental Engineering, University of California, One Shields Avenue, Davis, CA 95616, U.S.A.
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Abstract

In this paper, we establish a link between maximizing (information-theoretic) entropy and the construction of polygonal interpolants. The determination of shape functions on n-gons (n>3) leads to a non-unique under-determined system of linear equations. The barycentric co-ordinates ϕi, which form a partition of unity, are associated with discrete probability measures, and the linear reproducing conditions are the counterpart of the expectations of a linear function. The ϕi are computed by maximizing the uncertainty H12,…,ϕn)=−∑math image ϕi logϕi, subject to the above constraints. The description is expository in nature, and the numerical results via the maximum entropy (MAXENT) formulation are compared to those obtained from a few distinct polygonal interpolants. The maximum entropy formulation leads to a feasible solution for ϕi in any convex or non-convex polygon. This study is an instance of the application of the maximum entropy principle, wherein least-biased inference is made on the basis of incomplete information. Copyright © 2004 John Wiley & Sons, Ltd.

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