I. Gargantini

The second Remes algorithm as originally established for polynomials, may converge or not when the approximating functions are rational. However, the few results known in this domain show how efficient the algorithm can be to obtain approximations with a small error, much more than in the polynomial case, in which the best approximation can be very nearly approached directly by a series development. The aim of this paper is to investigate the limitations of the applicability of certain extensions of the algorithm to the case where the approximations are rational as well as to present some numerical results.