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Inverse and saturation theorems for radial basis function interpolation
Author(s):
Robert
Schaback;
Holger
Wendland.
Journal:
Math. Comp.
71
(2002),
669-681.
MSC (2000):
Primary 41A05, 41A17, 41A27, 41A30, 41A40
Posted:
November 28, 2001
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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.
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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:
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
Posted:
November 28, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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