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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Inverse and saturation theorems for radial basis function interpolation


Authors: Robert Schaback and Holger Wendland
Journal: Math. Comp. 71 (2002), 669-681
MSC (2000): Primary 41A05, 41A17, 41A27, 41A30, 41A40
Published electronically: November 28, 2001
MathSciNet review: 1885620
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Abstract | References | Similar Articles | Additional Information

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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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
Email: wendland@math.uni-goettingen.de

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01383-7
PII: S 0025-5718(01)01383-7
Keywords: Positive definite functions, approximation orders
Received by editor(s): February 10, 2000
Published electronically: November 28, 2001
Article copyright: © Copyright 2001 American Mathematical Society