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Shape preserving approximation using least squares splines

Beliakov, Gleb 2000, Shape preserving approximation using least squares splines, Analysis in theory and applications, vol. 16, no. 4, pp. 80-98.

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Title Shape preserving approximation using least squares splines
Author(s) Beliakov, Gleb
Journal name Analysis in theory and applications
Volume number 16
Issue number 4
Start page 80
End page 98
Publisher Editorial Board of Analysis in Theory and Applications, Kluwer Academic Publishers
Place of publication Dordrecht, The Netherlands
Publication date 2000-12
ISSN 1672-4070
1573-8175
Keyword(s) least squares splines
monotone splines
monotone approximation
restricted least squares
Summary Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.
Notes The original publication can be found at www.springerlink.com
Language eng
Field of Research 010199 Pure Mathematics not elsewhere classified
HERDC Research category C1.1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2000, Springer
Persistent URL http://hdl.handle.net/10536/DRO/DU:30015933

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.