Algorithm for Constructing Simple Partial Fractions of the Best Approximation of Constants

详细

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 ρ_n − c, n ≥ n₀(c). We propose an algorithm for constructing the alternance and simple partial fraction of the best approximation of constants c.