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2008

Approximation on the sphere using radial basis functions plus polynomials

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Approximation on the sphere using radial basis functions plus polynomials
In this paper we analyse a hybrid approximation of functions on the sphere S2 R3 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. Key words. Scattered data, radial basis functions, spherical harmonics, error estimate. AMS subject classifications. 41A30, 65D30
Ian H. Sloan, Alvise Sommariva
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2008
Where ADCM
Authors Ian H. Sloan, Alvise Sommariva
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