A (tiny) library for finding rational approximations to arbitrary functions, using nonlinear least squares!
In a Julia REPL, type
julia>]add https://github.com/angeris/RationalApproximations.jl
To approximate the function exp(-x^2) in the range [-2, 2] with degree-three
polynomials in the numerator and denominator, you can write:
using RationalApproximations
x = range(-2, 2, length=100)
f(x) = exp(-x^2)
# Fit a rational approximation with degree 3 in the numerator and 3 in the denominator
poly = fit(x, f.(x), 3, 3)
f(.5)
# 0.7788007830714049
value(.5, poly)
# 0.7616562869126146You can, of course, plot the approximation against the true value:
(If you want better approximations, use higher degrees! ;)