Abstract
It is proved that for convex and centrally symmetric classes of functions a linear method is included among the best (in a definite sense) methods of approximation from values specified with an error at a finite number of points. For some of the simplest classes linear best methods are constructed and their error is estimated.
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K. Yu. Osipenko, “Optimal interpolation of analytic functions,” Matem. Zametki,12, No. 4, 465–476 (1972).
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N. S. Bakhvalov, “On optimal linear methods of approximation of operators on convex classes of functions,” Zh. Vychisl. Matem. i Matem. Fiz.,11, No. 4, 1014–1016 (1971).
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Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 359–368, March, 1975.
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Marchuk, A.G., Osipenko, K.Y. Best approximation of functions specified with an error at a finite number of points. Mathematical Notes of the Academy of Sciences of the USSR 17, 207–212 (1975). https://doi.org/10.1007/BF01149008
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DOI: https://doi.org/10.1007/BF01149008