Inverse and saturation theorems for radial basis function interpolation

Schaback, Robert; Wendland, Holger

doi:10.1090/S0025-5718-01-01383-7

Inverse and saturation theorems for radial basis function interpolation
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by Robert Schaback and Holger Wendland PDF

Math. Comp. 71 (2002), 669-681 Request permission

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.

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