Computational aspects of approximation to scattered data by using 'shifted' thin-plate splines

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A new multivariate approximation scheme to scattered data on arbitrary bounded domains in ℝd is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the 'shifted' thin-plate spline ('essentially,' since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless data, but its main advantage seems to be in the former case. We suggest an algorithm for the new approximation scheme with a detailed description (in a MATLAB-like program). Some numerical examples are presented along with comparisons with thin-plate spline interpolation and Wahba's thin-plate smoothing spline approximation.

Original languageEnglish
Pages (from-to)329-359
Number of pages31
JournalAdvances in Computational Mathematics
Issue number4
StatePublished - 2001

Bibliographical note

Funding Information:
I am grateful to Prof. Amos Ron for many helpful advices and suggestions which he offered during this work. This work was supported by Research Assistantships of Prof. Ron at University of Wisconsin-Madison (NSF Grant DMS-9626319 and the U.S. Army Research Office Contract DAAH04-95-1-0089). I would also like to express my appreciation to Prof. Carl de Boor for his help for the algorithm and numerical tests.


  • 'Shifted' thin-plate spline
  • Approximation order
  • Gauss elimination by degree
  • Radial basis function
  • Scattered data approximation


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