Smoothing Lipschitz functions

Beliakov, Gleb 2007, Smoothing Lipschitz functions, Optimization methods and software, vol. 22, no. 6, pp. 901-916, doi: 10.1080/10556780701393591.

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Title Smoothing Lipschitz functions
Author(s) Beliakov, GlebORCID iD for 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
Keyword(s) scattered data approximation
Lipschitz approximation
uniform approximation
constrained approximation
multivariate approximation
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:
Language eng
DOI 10.1080/10556780701393591
Field of Research 010303 Optimisation
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2007, Taylor & Francis
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