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
A. Kolmogoroff, “Über die besste Annäherung von Funktionen einer gegebenen Funktionenklasse,”Ann. Math.,37, 107–110 (1936).
V. M. Tikhomirov,Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow (1976).
N. P. Korneichuk,Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1987).
A. Pinkus,N-widths in Approximation Theory, Springer, Berlin (1985).
J. F. Traub and H. Wozniakowski,A General Theory of Optimal Algorithms, Academic Press, New York (1980).
J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski,Information, Uncertainty, Complexity, Addison-Wesley, London (1983).
A. G. Sukharev,Minimax Algorithms in Problems of Numerical Analysis [in Russian], Nauka (1989).
J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski,Information-Based Complexity, Academic Press, London (1988).
N. P. Korneichuk, “Informativeness of functionals,”Ukr. Mat. Zh.,46, No. 9, 1156–1163 (1994).
N. P. Korneichuk, “On the optimal encoding of elements of a metric space,”Ukr. Mat. Zh.,39, No. 2, 168–173 (1987).
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).
N. P. Korneichuk, “On passive and active algorithms for renewal of functions,”Ukr. Mat. Zh.,45, No. 2, 258–264 (1992).
N. P. Korneichuk, “Optimization of active algorithms for recovery of monotonic functions from Hölder class,”J. Complexity,10, 265–269 (1994).
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).
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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