- Title
- Uniform approximation by the highest defect continuous polynomial splines : Necessary and sufficient optimality conditions and their generalisations
- Creator
- Sukhorukova, Nadezda
- Date
- 2010
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/32105
- Identifier
- vital:3792
- Identifier
-
https://doi.org/10.1007/s10957-010-9715-0
- Identifier
- ISSN:0022-3239
- Abstract
- 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. © 2010 Springer Science+Business Media, LLC.
- Publisher
- Springer
- Relation
- Journal of Optimization Theory and Applications Vol. 147, no. 2 (2010), p. 378-394
- Rights
- Copyright Springer
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0103 Numerical and Computational Mathematics; 0102 Applied Mathematics; Chebyshev approximation; Nonsmooth optimisation; Polynomial splines with fixed knots; Quasidifferentials
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