On Local RBF Approximation

Details On Local RBF Approximation On Local RBF Approximation

2009-09-29

arxiv.org/abs/0909.5244v2

Mathematics

Classical Analysis and ODEs

14 pages, 1 figure. To appear in Adv. in Comp. Math

Scientific paper

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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