On the relation between the maximum errors of the least pth approximation and the minimax approximation by a rational function

摘要

This paper deals with the least pth approximation (p even) by a rational function and gives a theoretical lower bound for the ratio of the maximum error of the minimax approximation to that of the least pth approximation. Through numerical examples on various kinds of functions we verified that the above lower bound is a good estimation for the corresponding actual ratios. These results show that the least pth approximation for p=8 or 16 is usually enough to achieve a good approximation to the minimax approximation.