Inverse and saturation theorems for radial basis function interpolation

Authors:
Robert Schaback;Holger Wendland
Affiliations:
-;-
Venue:
Mathematics of Computation
Year:
2002

Citing 6
Cited 6

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Full length article: Lp Bernstein inequalities and inverse theorems for RBF approximation on Rd

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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.