Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1832–1840 | Cite as

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

  • N. P. Korneichuk


A problem of renewal of monotone functionsf(t) εHω[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 typeεα, 0<α<1, the valueN(ε) has a higher order asε→0 than in the nonadaptive case for the same amount of information.


Monotone Function Adaptive Algorithm Exact Estimate Nonadaptive Case 
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    A. G. Sukharev,Minimax Algorithms in Problems of Numerical Analysis [in Russian], Nauka, Moscow (1989).Google Scholar
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    N. P. Komeichuk, “On passive and active algorithms of function renewal,”Ukr. Mat. Zh. 45, No. 2, 258–264 (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • N. P. Korneichuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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