A Smooth Multivariate Interpolation Algorithm

John Guckenheimer ()
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John Guckenheimer: Cornell University, Department of Mathematics

A chapter in Essays in Mathematics and its Applications, 2012, pp 231-239 from Springer

Abstract: 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.

Keywords: Voronoi Diagram; Mesh Point; Interpolation Problem; Subdivision Scheme; Multivariate Function (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_9

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DOI: 10.1007/978-3-642-28821-0_9

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