ALGORITHM FOR CONSTRUCTING SIMPLE PARTIAL FRACTIONS OF THE BEST APPROXIMATION OF CONSTANTS

摘要

It is known that for the best uniform approximation of real constants c by simple partial fractions ρn of order n on a real segment it is necessary and sufficient to have an alternance of n + 1 points on this segment for the difference ρn — c, n ≥ n_0(c). We propose an algorithm for constructing the alternance and simple partial fraction of the best approximation of constants c. Bibliography: 10 titles.