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Uniform Approximation by the Highest Defect Continuous Polynomial Splines: Necessary and Sufficient Optimality Conditions and Their Generalisations

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posted on 2024-07-09, 16:30 authored by Nadezda SukhorukovaNadezda Sukhorukova
In this paper necessary and sufficient optimality conditions for uniform approximation of continuous functions by polynomial splines with fixed knots are derived. The obtained results are generalisations of the existing results obtained for polynomial approximation and polynomial spline approximation. The main result is two-fold. First, the generalisation of the existing results to the case when the degree of the polynomials, which compose polynomial splines, can vary from one subinterval to another. Second, the construction of necessary and sufficient optimality conditions for polynomial spline approximation with fixed values of the splines at one or both borders of the corresponding approximation interval.

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PDF (Accepted manuscript)

ISSN

0022-3239

Journal title

J Optim Theory Appl

Volume

147

Issue

2

Pagination

16 pp

Publisher

Springer

Copyright statement

Copyright © 2010 Springer Science+Business Media, LLC. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. The definitive version of the publication is available at www.springer.com.

Language

eng

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