On passive and active algorithms of reconstruction of functions

Abstract

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.