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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation order from bivariate $ C\sp{1}$-cubics: a counterexample


Authors: C. de Boor and K. Höllig
Journal: Proc. Amer. Math. Soc. 87 (1983), 649-655
MSC: Primary 41A15; Secondary 41A25, 41A63
MathSciNet review: 687634
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Abstract: It is shown that the space of bivariate $ {C^1}$ piecewise cubic functions on a hexagonal mesh of size $ h$ approximates to certain smooth functions only to within $ O({h^3})$ even though it contains a local partition of every cubic polynomial.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687634-4
PII: S 0002-9939(1983)0687634-4
Keywords: $ {\text{B}}$-splines, multivariate, spline functions, degree of approximation, pp, smooth
Article copyright: © Copyright 1983 American Mathematical Society