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arXiv · 0705.4300

Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

R. A. Brownlee
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Abstract

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.

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R. A. Brownlee. 2007-05-30. Error estimates for interpolation of rough data using the scattered shifts of a radial basis function. https://doi.org/10.1007/s11075-004-3620-2

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