On passive and active algorithms of reconstruction of functions - Korneichuk, N. P. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
We consider passive and active algorithms of reconstruction of functions, satisfying the condition |f(t′) − f(t″)| ≤ |t′ − t″|^α, 0 < α ≤ 1, according to their values f(t) at the points of the interval [a, b]. An active algorithm is presented which guarantees, for monotonic functions from the above-mentioned class with 0 < α < 1, a higher order of error in C [a, b] than can be attained by any passive algorithm.