I am pleased to announce a new version of RationalFunctionApproximation.jl, a package for the automatic approximation of functions by ratios of polynomials.
Unlike polynomials, rational function interpolants can use arbitrary node locations at high degree without suffering from Runge instability. The approximations can be made accurate to ten digits or more on arbitrary domains in the complex plane, in addition to ordinary intervals, even for functions that have nearly singular behavior.
In addition to the continuum AAA algorithm that was implemented in v0.1, the package now offers (1) linear least-squares approximation with prescribed poles (a la Trefethen and Costa) and (2) an implementation of the greedy Thiele continued-fraction interpolation suggested by Celis. The latter is interesting as an O(n^2) alternative to the O(n^4) runtime of AAA, although its stability is less consistent at the moment.
In addition, the package plays nicely with extended precision and is easily called from Python.
I invite you to check the documentation. Enjoy!
