Cardinal interpolation by multivariate splines

Chui, C. K.; Jetter, K.; Ward, J. D.

doi:10.1090/S0025-5718-1987-0878701-2

Cardinal interpolation by multivariate splines
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by C. K. Chui, K. Jetter and J. D. Ward PDF

Math. Comp. 48 (1987), 711-724 Request permission

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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Constructive Aspects of Functional Analysis