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Local radial basis function approximation on the sphere. (English)
Bull. Aust. Math. Soc. 77, No. 2, 197-224 (2008).
A local error estimate is established for zonal (radial) basis functions and put in comparison to a corresponding global (spherical) error estimate. The method of proof contains an application of the Videnskii inequality. The convergence order found is ${1\over 2}(s-1)$. Some numerical examples and an appendix with a proof detail complete the article.
Reviewer: Martin D. Buhmann (Gießen)