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Monotonicity preserving approximation of multivariate scattered data

Beliakov, Gleb 2005, Monotonicity preserving approximation of multivariate scattered data, BIT numerical mathematics, vol. 45, no. 4, pp. 653-677.

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Title Monotonicity preserving approximation of multivariate scattered data
Author(s) Beliakov, Gleb
Journal name BIT numerical mathematics
Volume number 45
Issue number 4
Start page 653
End page 677
Publisher Kluwer Academic Publishers
Place of publication Dordrecht, The Netherlands
Publication date 2005
ISSN 0006-3835
1572-9125
Keyword(s) monotone approximation
isotone approximation
scattered data
central algorithm
optimal approximation
Summary This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.
Notes The original publication can be found at www.springerlink.com
Language eng
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2005, Springer
Persistent URL http://hdl.handle.net/10536/DRO/DU:30003256

Document type: Journal Article
Collections: School of Information Technology
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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.