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) 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.