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Least squares splines with free knots: global optimization approach

Beliakov, Gleb 2004, Least squares splines with free knots: global optimization approach, Applied mathematics and computation, vol. 149, no. 3, pp. 783-798.

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Title Least squares splines with free knots: global optimization approach
Author(s) Beliakov, Gleb
Journal name Applied mathematics and computation
Volume number 149
Issue number 3
Start page 783
End page 798
Publisher Elsevier
Place of publication New York, NY
Publication date 2004-02-22
ISSN 0096-3003
1873-5649
Keyword(s) least squares splines
regression splines
splines with free knots
global optimisation
cutting angle method
Summary Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.


Notes This is a post-peer reviewed electronic version of an article published in Applied Mathematics and Computation. A link to the published version is provided below.
Language eng
Field of Research 010201 Approximation Theory and Asymptotic Methods
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2003, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30002355

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.