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On the accuracy of surface spline interpolation on the unit sphere

Hubbert, Simon and Morton, Tanya M. (2004) On the accuracy of surface spline interpolation on the unit sphere. In: Neamtu, M. and Saff, E.B. (eds.) Advances in Constructive Approximation: Vanderbild 2003. Brentwood,Tennessee: Nashboro Press, pp. 227-242. ISBN 0 972848 22 3.

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Abstract

This paper considers a novel modification to the surface splines that have previously been used on the unit sphere. The surface splines considered are a natural analogue of surface splines in IRd and possess a unique Fourier expansion in terms of an orthonormal basis of spherical harmonics. Knowing the decay of the associated Fourier coefficients is important because they enable error estimates for spherical interpolation. In this paper we explicitly compute the Fourier coefficients of the surface splines and employ a recent theoretical result [8] to provide a useful error bound. We illuminate our theoretical findings by performing numerical experiments on the sphere and also on the hemisphere.

Item Type: Book Section
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Sandra Plummer
Date Deposited: 25 Jul 2006
Last Modified: 17 Apr 2013 12:32
URI: http://eprints.bbk.ac.uk/id/eprint/398

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