Characterisation theorem for best polynomial spline approximation with free knots

Author:

Sukhorukova Nadezda,Ugon Julien

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 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

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5. Chebyshev approximation by spline functions with free knots;Mulansky, Bernd;IMA J. Numer. Anal.,1992

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