The Mathematical Institute, University of Oxford, Eprints Archive

How fast do radial basis function interpolants of analytic functions converge?

Platte, Rodrigo B. (2009) How fast do radial basis function interpolants of analytic functions converge? Technical Report. IMA Journal of Numerical Analysis. (Submitted)

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Abstract

The question in the title is answered using tools of potential theory. Convergence and divergence rates of interpolants of analytic functions on the unit interval are analyzed. The starting point is a complex variable contour integral formula for the remainder in RBF interpolation. We study a generalized Runge phenomenon and explore how the location of centers and affects convergence. Special attention is given to Gaussian and inverse quadratic radial functions, but some of the results can be extended to other smooth basis functions. Among other things, we prove that, under mild conditions, inverse quadratic RBF interpolants of functions that are analytic inside the strip $|Im(z)| < (1/2\epsilon)$, where $\epsilon$ is the shape parameter, converge exponentially.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:870
Deposited By:Lotti Ekert
Deposited On:17 Dec 2009 08:06
Last Modified:17 Dec 2009 08:06

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