Inverse and saturation theorems for radial basis function interpolation
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- by Robert Schaback and Holger Wendland PDF
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Abstract:
While direct theorems for interpolation with radial basis functions are intensively investigated, little is known about inverse theorems so far. This paper deals with both inverse and saturation theorems. For an inverse theorem we especially show that a function that can be approximated sufficiently fast must belong to the native space of the basis function in use. In case of thin plate spline interpolation we also give certain saturation theorems.References
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Additional Information
- Robert Schaback
- Affiliation: Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany
- Email: schaback@math.uni-goettingen.de
- Holger Wendland
- Affiliation: Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany
- MR Author ID: 602098
- Email: wendland@math.uni-goettingen.de
- Received by editor(s): February 10, 2000
- Published electronically: November 28, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 669-681
- MSC (2000): Primary 41A05, 41A17, 41A27, 41A30, 41A40
- DOI: https://doi.org/10.1090/S0025-5718-01-01383-7
- MathSciNet review: 1885620