Characterisation theorem for best polynomial spline approximation with free knots

Sukhorukova, Nadezda and Ugon, Julien 2017, Characterisation theorem for best polynomial spline approximation with free knots, Transactions of the American Mathematical Society, vol. 369, no. 9, pp. 6389-6405, doi: 10.1090/tran/6863.

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Title Characterisation theorem for best polynomial spline approximation with free knots
Author(s) Sukhorukova, Nadezda
Ugon, JulienORCID iD for Ugon, Julien
Journal name Transactions of the American Mathematical Society
Volume number 369
Issue number 9
Start page 6389
End page 6405
Total pages 17
Publisher American Mathematical Society
Place of publication Providence, R.I.
Publication date 2017-09
ISSN 0002-9947
Keyword(s) Science & Technology
Physical Sciences
Summary In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions. 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. We start from identifying a special property of the knots. Then, using this property, we construct a characterisation theorem for best free-knots polynomial spline approximation, which is stronger than the existing characterisation results, at least in the case when only continuity is required.
Language eng
DOI 10.1090/tran/6863
Field of Research 0101 Pure Mathematics
HERDC Research category C1.1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2017, American Mathematical Society.
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