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Almost Interpolation and Radial Basis Functions

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Modern Developments in Multivariate Approximation

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 145))

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Abstract

After a review of some basic facts for Radial Basis Interpolation, we introduce the idea of almost interpolation for RBF, and show that in this setting it is possible to enlarge quite a lot the set of basic radial functions that can be used as basis. Our main result provides a Schoenberg-Whitney type condition for almost interpolation sets.

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Author information

Authors and Affiliations

  1. Laboratoire Jean Leray, UMR 6629 CNRS & Université de Nantes, 2 rue de la Houssinière, 46-44322, Nantes, France

    Alain Le Méhauté

Authors
  1. Alain Le Méhauté
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Gerhard-Mercator-Universität Duisburg, 47048, Duisburg, Germany

    Werner Haussmann

  2. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593, Stuttgart, Germany

    Kurt Jetter

  3. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Manfred Reimer  & Joachim Stöckler  & 

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Méhauté, A.L. (2003). Almost Interpolation and Radial Basis Functions. In: Haussmann, W., Jetter, K., Reimer, M., Stöckler, J. (eds) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8067-1_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9427-2

  • Online ISBN: 978-3-0348-8067-1

  • eBook Packages: Springer Book Archive

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