Advances in Computational Mathematics

, Volume 29, Issue 2, pp 147–177 | Cite as

Approximation on the sphere using radial basis functions plus polynomials

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Abstract

In this paper we analyse a hybrid approximation of functions on the sphere \({\mathbb S}^2 \subset {\mathbb R}^3\) by radial basis functions combined with polynomials, with the radial basis functions assumed to be generated by a (strictly) positive definite kernel. The approximation is determined by interpolation at scattered data points, supplemented by side conditions on the coefficients to ensure a square linear system. The analysis is first carried out in the native space associated with the kernel (with no explicit polynomial component, and no side conditions). A more refined error estimate is obtained for functions in a still smaller space. Numerical calculations support the utility of this hybrid approximation.

Keywords

Scattered data Radial basis functions Spherical harmonics Error estimate 

Mathematics Subject Classifications (2000)

41A30 65D30 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.School of MathematicsUniversity of New South WalesSydneyAustralia

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