Optimization of adaptive algorithms for the renewal of monotone functions from the class $H^ω$ - Korneichuk, N. P. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
A problem of renewal of monotone functions $f(t) \in H^{ω}[a, b]$ 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 $N(ε)$ of steps providing the uniform $ε$-error. For moduli of continuity of type $εα, 0 < α < 1$, the value $N(ε)$ has a higher order as $ε → 0$ than in the nonadaptive case for the same amount of information.