The Differential Correction Algorithm for Rational $\ell _\infty $-Approximation

Abstract

The version of the “differential correction algorithm” that is most used at the present time is a modification of the original version, perhaps because it has been proved that the modified version has sure convergence properties. However, the purpose of this paper is to direct attention back to the original version. It is now proved that the original version also has sure convergence properties. Furthermore, we prove that its rate of convergence is quadratic. This makes it superior to the more popular, modified version of the algorithm. Some numerical examples are given to compare the two versions, and these leave little doubt that the original algorithm is much better in practice.