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An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points

  • Jean Meinguet
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

Abstract

The mathematical theory underlying the practical method of “surface spline interpolation” provides approximation theory with an intrinsic concept of multivariate spline ready for use. A proper abstract setting is shown to be some Hilbert function space, the reproducing kernel of which involves no functions more complicated than logarithms. The crux of the matter is that convenient representation forpiulas can be obtained by resorting to convolutions or to Fourier transforms of distributions.

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Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Jean Meinguet
    • 1
  1. 1.Institut de Mathématique Pure et Appliquée chemin du Cyclotron 2Université Catholique de LouvainLouvain-la-NeuveBelgium

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