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On the Best Approximation Properties of C ∞-Smooth Functions on an Interval of the Real Axis (to the Phenomenon of Unsaturated Numerical Methods)

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Abstract

In 1975 K. I. Babenko announced his discovery of conceptually new unsaturated numerical methods. They are distinguished by the absence of the principal error term, which results in their ability to adjust automatically to all natural correctness classes of problems (the phenomenon of unsaturated numerical methods). We show that the phenomenon of unsaturation of a numerical method on an interval is a consequence, although exceptionally subtle, of the well-developed theory of polynomial approximation to continuous functions. By the way, K. I. Babenko always insisted on that.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. N. Belykh

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  1. V. N. Belykh
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Original Russian Text Copyright © 2005 Belykh V. N.

The author was partially supported by the Russian Foundation for Basic Research (Grant 05-01-00250) and the program “Contemporary Problems in Mathematics” of the Division of Mathematical Sciences of the Russian Academy of Sciences.

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 483–499, May–June, 2005.

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Belykh, V.N. On the Best Approximation Properties of C ∞-Smooth Functions on an Interval of the Real Axis (to the Phenomenon of Unsaturated Numerical Methods). Sib Math J 46, 373–385 (2005). https://doi.org/10.1007/s11202-005-0040-z

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  • DOI: https://doi.org/10.1007/s11202-005-0040-z

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