Interpolation of Lipschitz functions

Beliakov, Gleb 2006, Interpolation of Lipschitz functions, Journal of computational and applied mathematics, vol. 196, no. 1, pp. 20-44, doi: 10.1016/

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Title Interpolation of Lipschitz functions
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb
Journal name Journal of computational and applied mathematics
Volume number 196
Issue number 1
Start page 20
End page 44
Publisher Elsevier B.V.
Place of publication Amsterdam, The Netherlands
Publication date 2006-11-01
ISSN 0377-0427
Keyword(s) scattered data interpolation
lipschitz approximation
optimal interpolation
central algorithm
multivariate approximation
Summary 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.
Notes 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.
Language eng
DOI 10.1016/
Field of Research 010301 Numerical Analysis
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2005, Elsevier
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