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

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.