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Journal of Optimization Theory and Applications

, Volume 147, Issue 2, pp 378–394 | Cite as

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

  • Nadezda Sukhorukova
Article

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.

Keywords

Nonsmooth optimisation Quasidifferentials Chebyshev approximation Polynomial splines with fixed knots 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Center for Informatics and Applied OptimizationUniversity of BallaratBallaratAustralia
  2. 2.CIAO, ITMSUniversity of BallaratBallaratAustralia

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