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Shepard's method of ``metric interpolation'' to bivariate and multivariate interpolation


Authors: William J. Gordon and James A. Wixom
Journal: Math. Comp. 32 (1978), 253-264
MSC: Primary 41A63
DOI: https://doi.org/10.1090/S0025-5718-1978-0458027-6
MathSciNet review: 0458027
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Abstract: Shepard developed a scheme for interpolation to arbitrarily spaced discrete bivariate data. This scheme provides an explicit global representation for an interpolant which satisfies a maximum principle and which reproduces constant functions. The interpolation method is basically an inverse distance formula which is generalized to any Euclidean metric. These techniques extend to include interpolation to partial derivative data at the interpolation points.


References [Enhancements On Off] (What's this?)

  • [1] P. J. DAVIS, Interpolation and Approximation, Dover, New York, 1975. MR 0380189 (52:1089)
  • [2] C. C. POEPPELMEIER, A Boolean Sum Interpolation Scheme to Random Data for Computer Aided Geometric Design, M. S. Thesis, University of Utah, 1975.
  • [3] L. L. SCHUMAKER, "Fitting surfaces to scattered data," Approximation Theory II (G. G. Lorentz, C. K. Chui & L. L. Schumaker, Editors), Academic Press, New York, 1976, pp. 203-268. MR 0426369 (54:14312)
  • [4] D. SHEPARD, "A two-dimensional interpolation function for irregularly-spaced data," Proc. 1968 ACM Nat. Confi., pp. 517-524.

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DOI: https://doi.org/10.1090/S0025-5718-1978-0458027-6
Article copyright: © Copyright 1978 American Mathematical Society

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