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Controlled approximation and a characterization of the local approximation order

Authors: C. de Boor and R.-Q. Jia
Journal: Proc. Amer. Math. Soc. 95 (1985), 547-553
MSC: Primary 41A25; Secondary 65N30
MathSciNet review: 810161
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Abstract: The local approximation order from a scale $ ({S_h})$ of approximating functions on $ {{\mathbf{R}}^m}$ is characterized in terms of the linear span (and its Fourier transform) of the finitely many compactly supported functions $ \varphi $ whose integer translates $ \varphi ( \cdot - j),j \in {z^m}$, span the space $ S = {S_1}$ from which the scale is derived. This provides a correction of similar results stated and proved, in part, by Strang and Fix.

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Keywords: Controlled approximation, approximation order, multivariate, box splines, finite element analysis, Fourier series
Article copyright: © Copyright 1985 American Mathematical Society