Approximation on the sphere using radial basis functions plus polynomials

Advances in Computational Mathematics

Volumn 29, Issue 2, 2008, Pages 147-177

  Sloan, Ian H ^a   Sommariva, Alvise ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Error estimate; Radial basis functions; Scattered data; Spherical harmonics

Indexed keywords

EID: 47249116177     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-007-9048-1     Document Type: Article

References (19)

1. Chen, D., Menegatto, V.A., Sun, X.: A necessary and sufficient condition for strictly positive definite functions on spheres. Proc. Amer. Math. Soc. 131, 2733-2740 (2003)
2. NASA.: The NASA GSFC and NIMA Joint Geopotential Model. http://cddis.gsfc.nasa.gov/926/egm96/ (1998)
3. Fasshauer, G.E., Schumaker, L.L.: Scattered data fitting on the sphere. In: Daehlen, M., Lyche, T., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces II, pp. 117-166. Vanderbilt University Press, Nashville, TN (1998)
4. Freeden, W.: On spherical spline interpolation and approximation. Math. Methods Appl. Sci. 3, 551-575 (1981)
5. Freeden, W., Gervens, T., Schreiner, M.: Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford Science (Clarendon), Oxford, UK (1998)
6. Freeden, W., Hermann, P.: Uniform approximation by spherical spline interpolation. Math. Z. 193, 265-275 (1986)
7. von Golitschek, M., Light, W.A.: Interpolation by polynomials and radial basis functions on spheres. Constr. Approx. 17, 1-18 (2001)
8. p -error estimates for radial basis function interpolation on the sphere. J. Approx. Theory 129, 58-77 (2004)
9. Jetter, K., Stöckler, J., Ward, J.: Error estimates for scattered data interpolation on spheres. Math. Comp. 68, 733-749 (1999)
10. Levesley, J., Light, W., Ragozin, D., Sun, X.: A simple approach to the variational theory for the interpolation on spheres. In: International Series of Numerical Mathematics vol. 132, pp. 117-143. Birkhauser Verlag, Basel (1999)
11. MAGSAT.: MAGSAT-NASA/United States Geological Survey (USGS) effort to measure near-earth magnetic fields on a global basis. http://nssdc.gsfc.nasa. gov/database/Master Catalog?sc=1979-094A (1979).
12. Reimer, M.: Multivariate polynomial approximation. In: International Series of Numerical Mathematics, vol. 144. Birkhauser Verlag, Basel (2003)
13. Schaback, R.: Native Hilbert spaces for radial basis functions I. In: International Series of Numerical Mathematics, vol. 132, pp. 255-282. Birkhauser Verlag, Basel (1999)
14. Schaback, R.: Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp. 68, 201-216 (1999)
15. Schoenberg, I.J.: Positive definite functions on the spheres. Duke Math. J. 9, 96-108 (1942)
16. Szegö, G.: Orthogonal polynomials. In: American Mathematical Society Colloquium Publications, 4th edn., vol. 23. American Mathematical Society, Providence, RI (1975)
17. Wahba, G.: Spline intepolation and smoothing on the sphere. SIAM J. Sci. Stat. Comput. 2, 5-16 (1981)
18. Wendland, H.: Scattered Data Approximation. In: Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge (2005)
19. Xu, Y., Cheney, E.W.: Strictly positive definite functions on spheres. Proc. Amer. Math. Soc. 116, 977-981 (1992)