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Error estimates for scattered data interpolation on spheres
Author(s):
Kurt
Jetter;
Joachim
Stöckler;
Joseph
D.
Ward.
Journal:
Math. Comp.
68
(1999),
733-747.
MSC (1991):
Primary 41A05, 41A25;
Secondary 41A30, 41A63
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Abstract:
We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the  -sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics. The Markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics.
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Additional Information:
Kurt
Jetter
Affiliation:
Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart
Email:
kjetter@uni-hohenheim.de
Joachim
Stöckler
Affiliation:
Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart
Email:
stockler@uni-hohenheim.de
Joseph
D.
Ward
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843
Email:
jward@math.tamu.edu
DOI:
10.1090/S0025-5718-99-01080-7
PII:
S 0025-5718(99)01080-7
Keywords:
Scattered data interpolation,
spherical harmonics,
Markov inequality,
norming set,
best approximation
Received by editor(s):
August 25, 1997
Additional Notes:
Research supported by NSF Grant DMS-9303705 and Air Force AFOSR Grant F49620-95-1-0194.
Copyright of article:
Copyright
1999,
American Mathematical Society
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