2019
Том 71
№ 11

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Optimization of adaptive algorithms for the renewal of monotone functions from the class $H^ω$

Korneichuk N. P.

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Abstract

A problem of renewal of monotone functions $f(t) \in H^{\omega}[a, b]$ with fixed values at the ends of an interval is studied by using adaptive algorithms for calculating the values of $f(t)$ at certain points. Asymptotically exact estimates unimprovable on the entire set of adaptive algorithms are obtained for the least possible number $N(\varepsilon)$ of steps providing the uniform $ε$-error. For moduli of continuity of type $εα, 0 < α < 1$, the value $N(\varepsilon)$ has a higher order as $ε → 0$ than in the nonadaptive case for the same amount of information.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 12, pp 1832-1840.

Citation Example: Korneichuk N. P. Optimization of adaptive algorithms for the renewal of monotone functions from the class $H^ω$ // Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1627–1634.

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