Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 49, Issue 1, Pages 103-130Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2005.01.010
Keywords
radial basis function; RBF; interpolation; polynomial unisolvency
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Multivariate interpolation of smooth data using smooth radial basis functions is considered. The behavior of the interpolants in the limit of nearly flat radial basis functions is studied both theoretically and numerically. Explicit criteria for different types of limits are given. Using the results for the limits, the dependence of the error on the shape parameter of the radial basis function is investigated. The mechanisms that determine the optimal shape parameter value are studied and explained through approximate expansions of the interpolation error. (C) 2005 Elsevier Ltd. All rights reserved.
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