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A Smooth Multivariate Interpolation Algorithm

In: Essays in Mathematics and its Applications

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  • John Guckenheimer

    (Cornell University, Department of Mathematics)

Abstract

This brief paper introduces an algorithm for smooth interpolation of a multivariate function. The input data for the algorithm consists of a set of function values and derivatives up to order r on a finite set of points E. The algorithm utilizes the Voronoi diagram of E to construct a partition of unity that isolates the points of E. Averaging locally defined functions with the partition of unity yields the interpolating function. There are no special cases; the algorithm treats all input data uniformly. The paper describes a test problem, the computation of a surface that is defined as the level set of a function of three variables. This test demonstrates that the algorithm produces approximations whose order corresponds to the degree of the derivatives in the input data.

Suggested Citation

  • John Guckenheimer, 2012. "A Smooth Multivariate Interpolation Algorithm," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Essays in Mathematics and its Applications, edition 127, pages 231-239, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-28821-0_9
    DOI: 10.1007/978-3-642-28821-0_9
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