Error estimates and condition numbers for radial basis function interpolation

Authors:
Robert Schaback
Affiliations:
Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, Germany D-37083
Venue:
Advances in Computational Mathematics
Year:
1995

Citing 10
Cited 2

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Norm estimates for the inverse of a general class of scattered-data radial-function interpolation matrices

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Lower bounds for norms of inverses of interpolation matrices for radial basis functions

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Abstract

For interpolation of scattered multivariate data by radial basis functions, an "uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich-Ward theory of upper bounds on the norm of the inverse of the interpolation matrix is presented in order to handle the whole set of radial basis functions that are currently in use.