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

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Abstract

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.

Original languageEnglish
Pages (from-to)227-247
Number of pages21
JournalConstructive Approximation
Volume17
Issue number2
DOIs
StatePublished - 2001

Keywords

  • "Shifted" surface
  • Approximation order
  • Multiquadrics
  • Radial basis function
  • Spline

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