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arXiv · 1412.2323

Characterization theorem for best polynomial spline approximation with free knots

Nadezda Sukhorukova·Julien Ugon
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Abstract

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 characterization theorem for best free knots polynomial spline approximation, which is stronger than the existing characterisation results when only continuity is required.

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Nadezda Sukhorukova, Julien Ugon. 2014-12-07. Characterization theorem for best polynomial spline approximation with free knots. https://doi.org/10.1090/tran%2F6863

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