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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A natural formulation of quasi-interpolation by multivariate splines

Authors: Charles K. Chui and Harvey Diamond
Journal: Proc. Amer. Math. Soc. 99 (1987), 643-646
MSC: Primary 41A15; Secondary 41A65
MathSciNet review: 877032
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Abstract: A quasi-interpolation formula based on discrete function values is given in the form of a multivariate spline series that yields the local approximation order characterized by the Fix-Strang conditions. This formula can be considered as a partial sum of the formal Neumann series expansion of the formal interpolation operator, and hence, justifies that "quasi-interpolation" is indeed an appropriate terminology for such an approximation formula.

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Keywords: Multivariate splines, local approximation order, quasi-interpolation, Neumann series
Article copyright: © Copyright 1987 American Mathematical Society