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Mathematics of Computation

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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
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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Keywords: Cardinal interpolation, scaled cardinal interpolation, Fourier transform, discrete Fourier transform, box splines, Marsden identity
Article copyright: © Copyright 1987 American Mathematical Society