beliakov-lipint-2005.pdf (1 MB)
Interpolation of Lipschitz functions
This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.
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Journal
Journal of computational and applied mathematicsVolume
196Issue
1Pagination
20 - 44Publisher
Elsevier B.V.Location
Amsterdam, The NetherlandsPublisher DOI
Link to full text
ISSN
0377-0427Language
engNotes
This nis a post-peer reviewed electronic version of an article published in the Journal of Computational and Applied Mathematics. A link to the published version is provided below.Publication classification
C1 Refereed article in a scholarly journalCopyright notice
2005, ElsevierUsage metrics
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