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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.

Keywords

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}
}
R2 v1 2026-07-01T08:12:29.186Z