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Approximation with Barycentric Coordinates the Hilbertian Case

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Multivariate Approximation Theory IV

Abstract

In this paper, we present a unified approach for the construction of a large class of piece-wise functions (which contain classical finite elements, polynomial and polyhedral splines). This approach is based on a general formalism which proceeds from algebraic topology and theory of Hilbertian Kernels. Here we can give only an overview of that technique.

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Bibliography

  1. M. ATTEI: Fonctions “spline” et méthodes d’éléments finis, RAIRO, 1975, pp. 13–40.

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  2. M. BOATTIN: Approximation en coordonnées barycentriques généralisées. Thesis January 1989 ( Université Paul Sabatier Toulouse).

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  3. W. DAHMEN and C.A. MICHELLI: Recent progress in multivariate splines, in Approximation Theory IV, eds. C.K. Chuff, L.L. Schumaker, J.D. Ward, Academic Press, 27–121, 1983.

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© 1989 Birkhäuser Verlag Basel

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Atteia, M. (1989). Approximation with Barycentric Coordinates the Hilbertian Case. In: Multivariate Approximation Theory IV. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7298-0_2

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  • DOI: https://doi.org/10.1007/978-3-0348-7298-0_2

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7300-0

  • Online ISBN: 978-3-0348-7298-0

  • eBook Packages: Springer Book Archive

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