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RobustPade.jl

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Julia implementation of the Pade approximation algorithm of P. Gonnet, S. Guettel, and L. N. Trefethen, "Robust Pade approximation via SVD", SIAM Rev., 55:101-117, 2013.

Installation

This package is unregistered, so may be added by

(v1.7) pkg> add https://github.com/mjp98/RobustPade.jl

This package supports Julia v1.7 and later.

Usage

julia> using RobustPade

Example

Construct a Pade approximant of $\exp$ of type $(2,2)$, returning a Polynomials.RationalFunction

julia> r = robustpade(exp,2, 2)
(1.0 + 0.4999999999999998*x + 0.08333333333333322*x^2) // (1.0 - 0.5000000000000002*x + 0.08333333333333347*x^2)

When the first argument is a function, TaylorSeries.taylor_expand is called to generate the taylor expansion from which the Pade approximation is computed.

Similar packages

Pade approximation algorithms are available in:

  • Polynomials.jl method is unstable - see this issue
  • SymPy's methods may be called, as described in this comment. The packages Wynn.jl and Pade.jl provide some methods for calculating epsilon tables using SymPy.

For more general rational approximation algorithms, see