Interpolation by polynomials and radial basis functions on spheres

Constructive Approximation

Volumn 17, Issue 1, 2001, Pages 1-18

  Golitschek, M V ^a   Light, W A ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Error estimates; Interpolation; Radial basis functions; Spheres; Spherical harmonics

Indexed keywords

EID: 0035529218     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003650010028     Document Type: Article

References (7)

1. J. DUCHON (1977): Splines minimizing rotation-invariant seminorms in Sobolev spaces. In: Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics 571 (W. Schempp and K. Zeller, eds.). Berlin: Springer-Verlag, pp. 85-100.
2. W. FREEDEN (1981): On spherical spline interpolation and approximation. Math. Methods Appl. Sci., 3:551-575.
3. W. FREEDEN, M. SCHREINER, R. FRANKE (1997): A survey on spherical spline approximation. Survey Math. Ind., 7:29-85.
4. J. LEVESLEY, W. LIGHT, D. RAGOSIN, X. SUN (1999): A simple approach to the variational theory for interpolation on spheres. In: New Developments in Approximation Theory (M.W. Müller, M.D. Buhmann, D.H. Mache, and M. Felten, eds.). ISNM International Series of Numerical Mathematics 132. Basel: Birkhäuser Verlag, pp. 109-116.
5. W. MADYCH, S. NELSON (1988): Multivariate interpolation and conditionally positive definite functions. Approx. Theory Appl., 4:77-89.
6. C. MÜLLER (1966): Spherical Harmonics. Lecture Notes in Mathematics 17. Berlin: Springer-Verlag.
7. G. WAHBA (1981): Spline interpolation and smoothing on the sphere. SIAM J. Sci. Statist. Comput., 2:5-16.