Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation
HTML articles powered by AMS MathViewer
- by William J. Gordon and James A. Wixom PDF
- Math. Comp. 32 (1978), 253-264 Request permission
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
- Philip J. Davis, Interpolation and approximation, Dover Publications, Inc., New York, 1975. Republication, with minor corrections, of the 1963 original, with a new preface and bibliography. MR 0380189 C. C. POEPPELMEIER, A Boolean Sum Interpolation Scheme to Random Data for Computer Aided Geometric Design, M. S. Thesis, University of Utah, 1975.
- Larry L. Schumaker, Fitting surfaces to scattered data, Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976) Academic Press, New York, 1976, pp. 203–268. MR 0426369 D. SHEPARD, "A two-dimensional interpolation function for irregularly-spaced data," Proc. 1968 ACM Nat. Confi., pp. 517-524.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 253-264
- MSC: Primary 41A63
- DOI: https://doi.org/10.1090/S0025-5718-1978-0458027-6
- MathSciNet review: 0458027