Smoothing Lipschitz functions

Beliakov, Gleb 2007, Smoothing Lipschitz functions, Optimization methods and software, vol. 22, no. 6, pp. 901-916.


Title Smoothing Lipschitz functions
Author(s) Beliakov, Gleb
Journal name Optimization methods and software
Volume number 22
Issue number 6
Start page 901
End page 916
Publisher Taylor & Francis
Place of publication Abingdon, England
Publication date 2007-12
ISSN 1055-6788
1029-4937
Keyword(s) scattered data approximation
Lipschitz approximation
uniform approximation
constrained approximation
multivariate approximation
smoothing
Summary This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties of f. Depending on the assumptions about the distribution of the random noise, smoothing is reduced to a standard quadratic or a linear programming problem. We discuss an efficient algorithm which eliminates the redundant inequality constraints. Numerical experiments illustrate applicability and efficiency of the method. This approach provides an efficient new tool of multivariate scattered data approximation.
Notes This is an electronic version of an article published in Optimization methods and software, vol. 22, no. 6, pp. 901-916. Optimization Methods and Software is available online at: http://www.informaworld.com/openurl?genre=article&issn=1055-6788&volume=22&issue=6&spage=901
Language eng
Field of Research 010303 Optimisation
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2007, Taylor & Francis
Persistent URL http://hdl.handle.net/10536/DRO/DU:30007578

Document type: Journal Article
Collection: School of Engineering and Information Technology
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