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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
March 27, 1997. Dates revised: March 19, 1998; August 5, 1999. Date accepted: December 15, 1999.
Rights and permissions
About this article
Cite this article
Golitschek, M., Light, W. Interpolation by Polynomials and Radial Basis Functions on Spheres. Constr. Approx. 17, 1–18 (2001). https://doi.org/10.1007/s003650010028
Published:
Issue Date:
DOI: https://doi.org/10.1007/s003650010028