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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximation order from bivariate $C^{1}$-cubics: a counterexample
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by C. de Boor and K. Höllig PDF
Proc. Amer. Math. Soc. 87 (1983), 649-655 Request permission


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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  • G. Farin, Subsplines über Dreiecken, Dissertation, Braunschweig, 1979.
  • P. O. Frederickson, Quasi-interpolation, extrapolation, and approximation on the plane, Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971) Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971, pp. 159–167. MR 0336170
  • Malcolm Arthur Sabin, The use of piecewise forms for the numerical representation of shape, Tanulmányok—MTA Számitástech. Automat. Kutató Int. Budapest 60 (1977), 125. MR 656152
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 87 (1983), 649-655
  • MSC: Primary 41A15; Secondary 41A25, 41A63
  • DOI:
  • MathSciNet review: 687634