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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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  • Nadezda Sukhorukova

    (University of Ballarat
    University of Ballarat)

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.

Suggested Citation

  • Nadezda Sukhorukova, 2010. "Uniform Approximation by the Highest Defect Continuous Polynomial Splines: Necessary and Sufficient Optimality Conditions and Their Generalisations," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 378-394, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9715-0
    DOI: 10.1007/s10957-010-9715-0
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    Citations

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    Cited by:

    1. Jean-Pierre Crouzeix & Nadezda Sukhorukova & Julien Ugon, 2017. "Characterization Theorem for Best Polynomial Spline Approximation with Free Knots, Variable Degree and Fixed Tails," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 950-964, March.
    2. Nadezda Sukhorukova & Julien Ugon, 2016. "Chebyshev Approximation by Linear Combinations of Fixed Knot Polynomial Splines with Weighting Functions," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 536-549, November.
    3. Peiris, V. & Sharon, N. & Sukhorukova, N. & Ugon, J., 2021. "Generalised rational approximation and its application to improve deep learning classifiers," Applied Mathematics and Computation, Elsevier, vol. 389(C).

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