Characterization Theorem for Best Polynomial Spline Approximation with Free Knots, Variable Degree and Fixed Tails
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- 作者：Jean-Pierre Crouzeix ; Nadezda Sukhorukova…
- 关键词：Polynomial splines ; Chebyshev approximation ; Free knots ; Quasidifferential ; Best approximation conditions
- 刊名：Journal of Optimization Theory and Applications
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：172
- 期：3
- 页码：950-964
- 全文大小：
- 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
- 出版者：Springer US
- ISSN：1573-2878
- 卷排序：172
文摘
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). 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. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.