Interpolation by Polynomials and Radial Basis Functions on Spheres |
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Authors: | M v Golitschek W A Light |
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Institution: | M. v. Golitschek Institut für Angewandte Mathematik und Statistik Universit?t Würzburg Am Hubland 97074 Würzburg Germany, DE
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Abstract: | The paper obtains error estimates for approximation by radial basis functions on the sphere. The approximations are generated
by interpolation at scattered points on the sphere. The estimate is given in terms of the appropriate power of the fill distance
for the interpolation points, in a similar manner to the estimates for interpolation in Euclidean space. A fundamental ingredient
of our work is an estimate for the Lebesgue constant associated with certain interpolation processes by spherical harmonics.
These interpolation processes take place in ``spherical caps' whose size is controlled by the fill distance, and the important
aim is to keep the relevant Lebesgue constant bounded. This result seems to us to be of independent interest.
March 27, 1997. Dates revised: March 19, 1998; August 5, 1999. Date accepted: December 15, 1999. |
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Keywords: | , Radial basis functions, Spheres, Interpolation, Error estimates, Spherical harmonics, AMS Classification, 41A05,,,,,,41A25, 41A63, |
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