Uniform Approximation by the Highest Defect Continuous Polynomial Splines: Necessary and Sufficient Optimality Conditions and Their Generalisations |
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Authors: | Nadezda Sukhorukova |
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Institution: | (1) Department of Mathematics, International University of Hochiminh City, Thu Duc, Hochiminh City, Vietnam;(2) Department of Mathematics, University of Natural Sciences of Hochiminh City, Hochiminh City, Vietnam |
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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. |
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Keywords: | |
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