Pade' Approximant

Computes coefficients of Pade' Approximants to symbolic functions.

Description

This script will compute the coefficients for the "symmetric" Pade' approximant to a symbolic function expanded at x=0. It also returns poles and zeros to ensure that the expansion does not have undesireable behavior in the region of interest. Users may modify and redistribute this script freely.

• MATLAB release: MATLAB 6.0 (R12)

[Ymonnet Frederic]

I search all data on pade approximant for a personnel work in french universitie

[Jörg Kubitz]

a usefull thing
the documentation about y is wrong tho

[Taekjung Kim]

 

[Michael Ktistakis]

The code fails in cases the highest order coeffs are zero. (example: f=acos(x))

fser=taylor(f,0,Nc);
% Extract the expansion coefficients
c=sym2poly(fser)';
% Check that c includes the
% high order zero coeffs
if length(c) < Nc
    c = [zeros(Nc-length(c),1);c];
end
% Reverse the order (ascending powers)
c=c(Nc:-1:1);

[Johannes]

Is it fixable to meet atan(x) ?
And will it hold for all real values in the rage of [-inf +inf]?
I have code in the hand that could also compute unsymmetric pade approximants but I only use it for exp(x). I yet did not have the time to try implementing it for symbolic functions. The expantion point can be defined on input already. I am interested on getting approximants for the arcustangens(x) Function that hold for all real values.

[Wei Zhao]

would be better if it could expand in any point