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Optimization of adaptive algorithms for the renewal of monotone functions from the classHω

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Ukrainian Mathematical Journal Aims and scope

Abstract

A problem of renewal of monotone functionsf(t) εH ω[a, b] with fixed values at the ends of an interval is studied by using adaptive algorithms for calculating the values off(t) at certain points. Asymptotically exact estimates unimprovable on the entire set of adaptive algorithms are obtained for the least possible numberN(ε) of steps providing the uniformε-error. For moduli of continuity of typeε α, 0<α<1, the valueN(ε) has a higher order asε→0 than in the nonadaptive case for the same amount of information.

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References

  1. J. F. Traub and H. Wozniakowski,A General Theory of Optimal Algorithms, Academic Press, San Diego, CA (1980).

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  2. A. G. Sukharev,Minimax Algorithms in Problems of Numerical Analysis [in Russian], Nauka, Moscow (1989).

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  3. N. P. Komeichuk, “On passive and active algorithms of function renewal,”Ukr. Mat. Zh. 45, No. 2, 258–264 (1992).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. P. Korneichuk

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  1. N. P. Korneichuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1627–1634, December, 1993.

The work was supported by the Foundation for Fundamental Studies of Ukrainian State Committee for Science and Technology.

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Korneichuk, N.P. Optimization of adaptive algorithms for the renewal of monotone functions from the classHω. Ukr Math J 45, 1832–1840 (1993). https://doi.org/10.1007/BF01061353

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  • DOI: https://doi.org/10.1007/BF01061353

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