Cardinal interpolation by multivariate splines

Authors:
C. K. Chui, K. Jetter and J. D. Ward

Journal:
Math. Comp. **48** (1987), 711-724

MSC:
Primary 41A05; Secondary 41A15, 41A63

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878701-2

MathSciNet review:
878701

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Abstract: The purpose of this paper is to investigate cardinal interpolation using locally supported piecewise polynomials. In particular, the notion of a commutator is introduced and its connection with the Marsden identity is observed. The order of a commutator is shown to be equivalent to the Strang and Fix conditions that arise in the study of the local approximation orders using quasi-interpolants. We also prove that scaled cardinal interpolants give these local approximation orders.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878701-2

Keywords:
Cardinal interpolation,
scaled cardinal interpolation,
Fourier transform,
discrete Fourier transform,
box splines,
Marsden identity

Article copyright:
© Copyright 1987
American Mathematical Society