Bulletin Géodésique

, Volume 53, Issue 4, pp 273–289 | Cite as

Analytical collocation with kernel functions

  • D. Lelgemann


T. Krarup proposed the use of collocation with kernel functions for the approximation of a potential function on the earth surface as well as in local regions of a sphere. Starting from the smoothing criterion of the least norm of the horizontal gradients on a sphere, a neighbourhood criterion was derived taking into account smoothness as well as stability properties of the series evaluation. It is finally shown how to choose the kernel functions in order to obtain a smooth interpolation function at the surface of the earth.


Kernel Function Spherical Harmonic Series Evaluation Interpolation Function Horizontal Gradient 
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Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1979

Authors and Affiliations

  • D. Lelgemann
    • 1
  1. 1.Institut für Angewandte Geodäsie (Abtig. II DGFI) and Sonderforschungsbereich Satellitengeodäsie der TU München (SFB 78)MünchenGemany

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