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Information widths

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Ukrainian Mathematical Journal Aims and scope

Abstract

We introduce the notions of adaptive information widths of a set in a metric space and consider the problem of comparing them with nonadaptive widths. Exact results are obtained for one class of continuous functions that is not centrally symmetric.

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References

  1. A. Kolmogoroff, “Über die besste Annäherung von Funktionen einer gegebenen Funktionenklasse,”Ann. Math.,37, 107–110 (1936).

    Google Scholar 

  2. V. M. Tikhomirov,Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow (1976).

    Google Scholar 

  3. N. P. Korneichuk,Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  4. A. Pinkus,N-widths in Approximation Theory, Springer, Berlin (1985).

    Google Scholar 

  5. J. F. Traub and H. Wozniakowski,A General Theory of Optimal Algorithms, Academic Press, New York (1980).

    Google Scholar 

  6. J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski,Information, Uncertainty, Complexity, Addison-Wesley, London (1983).

    Google Scholar 

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

  8. J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski,Information-Based Complexity, Academic Press, London (1988).

    Google Scholar 

  9. N. P. Korneichuk, “Informativeness of functionals,”Ukr. Mat. Zh.,46, No. 9, 1156–1163 (1994).

    Google Scholar 

  10. N. P. Korneichuk, “On the optimal encoding of elements of a metric space,”Ukr. Mat. Zh.,39, No. 2, 168–173 (1987).

    Google Scholar 

  11. N. P. Korneichuk, “Widths of classes of continuous and differentiable functions inL p and optimal methods for encoding and renewal of functions and their derivatives,”Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 2, 266–290 (1981).

    Google Scholar 

  12. N. P. Korneichuk, “On passive and active algorithms for renewal of functions,”Ukr. Mat. Zh.,45, No. 2, 258–264 (1992).

    Google Scholar 

  13. N. P. Korneichuk, “Optimization of active algorithms for recovery of monotonic functions from Hölder class,”J. Complexity,10, 265–269 (1994).

    Google Scholar 

  14. N. P. Korneichuk, “Optimization of adaptive algorithms for the renewal of monotone functions from the classH ω,” Ukr. Mat. Zh.,45, No. 12, 1627–1634 (1993).

    Google Scholar 

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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. 47, No. 11, pp. 1506–1518, November, 1995.

This work was partially supported by the International Science Foundation, Grant UB 1000.

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Korneichuk, N.P. Information widths. Ukr Math J 47, 1720–1732 (1995). https://doi.org/10.1007/BF01057920

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  • DOI: https://doi.org/10.1007/BF01057920

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