Оптимизация адаптивных алгоритмов восстановления монотонных функций класса Hω

Abstract

A problem of recovery of monotone functions f(t) ∈ Hω[a,b] with fixed values at the ends of an interval is studied by using the adaptive algorithms for getting the values of f(t) at certain points. The asymptotically exact estimates, unimprovable on the whole of the set of adaptive algorithms, are obtained for the minimal possible number N(ε) of steps guaranteeing the uniform ε-error.