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Multivariate interpolation with increasingly flat radial basis functions of finite smoothness. (English) Zbl 1250.41002

Summary: We consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in \(\mathbb R^{d }\) 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.

MSC:

41A05 Interpolation in approximation theory
41A15 Spline approximation
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
41A63 Multidimensional problems

Software:

Matlab; rbf_qr
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Full Text: DOI

References:

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