Rational approximation of the absolute value function from measurements: a numerical study of recent methods

Understand

In this work, we propose an extensive numerical study on approximating the absolute value function.

• The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g., the Loewner framework and the AAA algorithm.
• Moreover, these methods are based on data, i.e., measurements of the original function (hence data-driven nature).
• We compare numerical results for these two methods with those of a recently-proposed best rational approximation method (the minimax algorithm) and with various classical bounds from the previous century.