Abstract
The problem is considered of constructing a least-width strip with a polynomial axis that contains the graph of a given continuous segment function. Convex analysis methods are used to obtain a criterion for solving the problem in a form comparable to the Chebyshev alternance. Sufficient conditions for the uniqueness of a solution are given, including those taking into account the differential properties of the segment function to be estimated.
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Original Russian Text © I.Yu. Vygodchikova, S.I. Dudov, E.V. Sorin, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 7, pp. 1175–1183.
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Vygodchikova, I.Y., Dudov, S.I. & Sorin, E.V. External estimation of a segment function by a polynomial strip. Comput. Math. and Math. Phys. 49, 1119–1127 (2009). https://doi.org/10.1134/S0965542509070057
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DOI: https://doi.org/10.1134/S0965542509070057