Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Characterisation theorem for best polynomial spline approximation with free knots


Authors: Nadezda Sukhorukova and Julien Ugon
Journal: Trans. Amer. Math. Soc. 369 (2017), 6389-6405
MSC (2010): Primary 49J52, 90C26, 41A15, 41A50
DOI: https://doi.org/10.1090/tran/6863
Published electronically: March 17, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 49J52, 90C26, 41A15, 41A50

Retrieve articles in all journals with MSC (2010): 49J52, 90C26, 41A15, 41A50


Additional Information

Nadezda Sukhorukova
Affiliation: Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
Address at time of publication: Faculty of Science, Federation University, P.O. Box 663, Ballarat, Victoria 3353, Australia
Email: nsukhorukova@swin.edu.au

Julien Ugon
Affiliation: Centre for Informatics and Applied Optimization, Federation University, P.O. Box 663, Ballarat, Victoria 3353, Australia
Email: j.ugon@federation.edu.au

DOI: https://doi.org/10.1090/tran/6863
Received by editor(s): September 17, 2013
Received by editor(s) in revised form: September 18, 2013, and September 27, 2015
Published electronically: March 17, 2017
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society