- Title
- Characterization theorem for best polynomial spline approximation with free knots, variable degree and fixed tails
- Creator
- Crouzeix, Jean-Pierre; Sukhorukova, Nadezda; Ugon, Julien
- Date
- 2017
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159295
- Identifier
- vital:11946
- Identifier
-
https://doi.org/10.1007/s10957-016-1048-1
- Identifier
- ISSN:0022-3239
- Abstract
- In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov-Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.
- Publisher
- Springer
- Relation
- Journal of Optimization Theory and Applications Vol. 172, no. 3 (2017), p. 950-964
- Rights
- Copyright © Springer Science+Business Media New York 2017
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0906 Electrical and Electronic Engineering; Polynomial splines; Chebyshev approximation; Free knots; Quasidifferential; Best approximation conditions
- Full Text
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