Abstract
The purpose of this paper is to investigate RBF approximation with highly nonuniform centers. Recently, DeVore and Ron have developed a notion of the local density of a set of centers—a notion that permits precise pointwise error estimates for surface spline approximation. We give an equivalent, alternative characterization of local density, one that allows effective placement of centers at different resolutions. We compare, also, the pointwise results of DeVore–Ron to previously works of Wu and Schaback and of Duchon.
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Communicated by Robert Schaback.
This research was done while the author was at Texas A&M University.
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Hangelbroek, T. On local RBF approximation. Adv Comput Math 37, 285–299 (2012). https://doi.org/10.1007/s10444-011-9212-5
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DOI: https://doi.org/10.1007/s10444-011-9212-5
Keywords
- Error estimates
- Nonlinear approximation
- Optimal approximation
- Radial basis functions
- Scattered data
- Thin-plate splines
- Surface splines
- Approximation order