Characterization theorem for best polynomial spline approximation with free knots
Optimization and Control
2025-01-30 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1412.2323,
title = {Characterization theorem for best polynomial spline approximation with free knots},
author = {Nadezda Sukhorukova and Julien Ugon},
journal= {arXiv preprint arXiv:1412.2323},
year = {2025}
}