RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains
Numerical Analysis
2025-12-09 v1 Numerical Analysis
Complex Variables
Abstract
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest in computational rational approximation. The \textsf{RationalFunctionApproximation} package supplies the fastest known implementations of these methods and the only arbitrary-precision ones. Combined with the \textsf{ComplexRegions} package, it can produce compact and accurate representations of a huge variety of functions over intervals, circles, or other domains in the complex plane.
Cite
@article{arxiv.2512.06140,
title = {RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains},
author = {Tobin A. Driscoll},
journal= {arXiv preprint arXiv:2512.06140},
year = {2025}
}