On passive and active algorithms of reconstruction of functions (Q1332052)

Two interpolation algorithms for continuous functions on a finite interval, satisfying a Hölder condition, are studied. The first, so called ``passive'', uses the arbitrary choice of the interpolating nodes. The second, ``active'', chooses the nodes step by step, taking into account the previously considered values. The active algorithm guarantees the great precision for monotonic functions fromt the above class.