RationalFunctionApproximation.jl

This Julia package adaptively computes rational approximations (i.e., ratios of polynomials) for functions on intervals and other domains in the complex plane.

The documentation includes a walkthrough showing off the main capabilities of the package.

Related work

• The Polynomials package provides rational functions, but not in a way related to function approximation.
• The BaryRational package implements the original (fully discrete) version of the AAA algorithm, as well as Floater–Hormann rational interpolation.
• The ApproxFun package provides 1D and multidimensional function approximation using Chebyshev polynomials and Fourier series. It also has extensive functionality for manipulating the approximations and for solving differential equations.
• There is an ApproxFunRational package, but it is undocumented.