Characterization theorem for best polynomial spline approximation with free knots
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866912208837935104 |
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| author | Sukhorukova, Nadezda Ugon, Julien |
| author_facet | Sukhorukova, Nadezda Ugon, Julien |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1412_2323 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Characterization theorem for best polynomial spline approximation with free knots Sukhorukova, Nadezda Ugon, Julien Optimization and Control Numerical Analysis 49J52, 90C26, 41A15, 41A50 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. |
| title | Characterization theorem for best polynomial spline approximation with free knots |
| topic | Optimization and Control Numerical Analysis 49J52, 90C26, 41A15, 41A50 |
| url | https://arxiv.org/abs/1412.2323 |