Multivariate interpolation with increasingly flat radial basis functions of finite smoothness

In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in ℝ d with finite smoothness of even order converge to a polyharmonic spline interpolant as the scale parameter of the radial ba...

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Bibliographic Details
Published in:Advances in computational mathematics 2012-04, Vol.36 (3), p.485-501
Main Authors: Song, Guohui, Riddle, John, Fasshauer, Gregory E., Hickernell, Fred J.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
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Summary:In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in ℝ d with finite smoothness of even order converge to a polyharmonic spline interpolant as the scale parameter of the radial basis functions goes to zero, i.e., the radial basis functions become increasingly flat.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-011-9192-5