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Cardinal interpolation by multivariate splines. (English) Zbl 0619.41004
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.

41A05 Interpolation in approximation theory
41A15 Spline approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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