Approximation order from bivariate 𝐶¹-cubics: a counterexample-Reference-Cited by-同舟云学术

Approximation order from bivariate 𝐶¹-cubics: a counterexample

Published:1983 Issue:4 Volume:87 Page:649-655
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

de Boor C.,Höllig K.

Abstract

It is shown that the space of bivariate C 1 {C^1} piecewise cubic functions on a hexagonal mesh of size h h approximates to certain smooth functions only to within O ( h 3 ) O({h^3}) even though it contains a local partition of every cubic polynomial.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1983-087-04/S0002-9939-1983-0687634-4/S0002-9939-1983-0687634-4.pdf

Reference8 articles.

1. Approximation by smooth multivariate splines;de Boor, C.;Trans. Amer. Math. Soc.,1983

2. C. de Boor and K. Höllig, 𝐵-splines from parallelepipeds, MRC TSR #2320, 1982.

3. \bysame, Bivariate box splines and smooth 𝑝𝑝 functions on a three-direction mesh, MRC TSR #2389; J. Comput. Appl. Math. (to appear).

4. de Casteljau, Courbes et surfaces à pôles, "Enveloppe 40.040", Institut National de la Propriété Industrielle, Paris, 1959.

5. Approximation by linear combinations of multivariate 𝐵-splines;Dahmen, Wolfgang;J. Approx. Theory,1981

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