Lp-error estimates for "shifted" surface spline interpolation on Sobolev space

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The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order 1 ≤ p ≤ ∞) of interpolation to functions in the Sobolev space Wpk (Ω) with k > max(0, d/2 - d/p). We are particularly interested in using the "shifted" surface spline, which actually includes the cases of the multiquadric and the surface spline. Moreover, we show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met.

Original languageEnglish
Pages (from-to)1349-1367
Number of pages19
JournalMathematics of Computation
Issue number243
StatePublished - Jul 2003


  • "Shifted" surface spline
  • Interpolation
  • Radial basis function
  • Surface spline


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