Two Simple Algorithms for Discrete Rational Approximation

This paper reports on computational experience with algorithms due to Loeb and Appel for rational approximation on discrete point sets. Following a brief review of the linear discrete approximation problem, the two rational algorithms are stated in a general setting. Finally, several numerical examples of applications to ${l_1}$, ${l_2}$, and ${l_\infty }$ approximation are supplied and discussed.