Approximation in Lp(Rd) from a space spanned by the scattered shifts of a radial basis function
- Cite this article as:
- Yoon, J. Constr. Approx (2001) 17: 227. doi:10.1007/s003650010033
- 48 Downloads
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.