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ChebPade.jl

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A Julia package to compute the Chebyshev-Pade approximation from a Chebyshev polynomial expansion.

Installation

This package is unregistered, so may be added by

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

This package supports Julia v1.7 and later.

Usage

julia> using ChebPade, ApproxFun

Example

Construct a Chebyshev-Pade approximant of the exponential function of type (2,2), returning the numerator and denominator of type ApproxFun.Fun

julia> f = Fun(exp,-1..1)
Fun(Chebyshev(-1..1),[1.2660658777520084, 1.1303182079849703, 0.27149533953407656, 0.04433684984866379, 0.0054742404420936785, 0.0005429263119139232, 4.497732295427654e-5, 3.19843646253781e-6, 1.992124804817033e-7, 1.1036771869970875e-8, 5.505896578301994e-10, 2.4979607981699334e-11, 1.0391104209722668e-12, 3.993680386393805e-14])

julia> p,q = chebpade(f,2,2)
(Fun(Chebyshev(-1..1),[1.0020016925359065, 0.48492995699568886, 0.04024039039994624]), Fun(Chebyshev(-1..1),[1.0, -0.47643278089764673, 0.038277919301135936]))

julia> using LinearAlgebra; p./q - f |> norm
9.313144965137737e-5

To do:

  • improve matrix construction to reduce allocations
  • optimise matrix inversion, e.g. inplace