Constructive Approximation

, Volume 17, Issue 2, pp 227–247

Approximation in Lp(Rd) from a space spanned by the scattered shifts of a radial basis function


DOI: 10.1007/s003650010033

Cite this article as:
Yoon, J. Constr. Approx (2001) 17: 227. doi:10.1007/s003650010033


A new multivariate approximation scheme on Rd using scattered translates of the “shifted” surface spline function is developed. The scheme is shown to provide spectral Lp-approximation orders with 1 ≤ p ≤ ∞, i.e., approximation orders that depend on the smoothness of the approximands. In addition, it applies to noisy data as well as noiseless data. A numerical example is presented with a comparison between the new scheme and the surface spline interpolation method.

AMS classification

41A15 41A25 41A30 41A63 

Key words and phrases

Radial basis function Approximation order “Shifted” surface Spline Multiquadrics 

Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • J. Yoon
    • 1
  1. 1.Department of Applied Mathematics, School of Mathematical SciencesTel-Aviv UniversityTel-AvivIsrael

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