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Smoothing Lipschitz functions

journal contribution
posted on 2007-12-01, 00:00 authored by Gleb BeliakovGleb Beliakov
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.

History

Journal

Optimization methods and software

Volume

22

Pagination

901-916

Location

Abingdon, England

ISSN

1055-6788

eISSN

1029-4937

Language

eng

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

Publication classification

C1 Refereed article in a scholarly journal, C Journal article

Copyright notice

2007, Taylor & Francis

Issue

6

Publisher

Taylor & Francis