Bill Allombert on Mon, 24 Oct 2011 22:53:21 +0200


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Re: Computing Padé approximants 

On Mon, Oct 24, 2011 at 06:44:48PM +0200, Sara Costa wrote:
> For my work I need to compute the Padé approximants of a holomorphic
> function around 0. I do not know the exact value of the coefficients of its
> Maclaurin series because they are the solution of a linear system.
> 
> I would like to know if there exists any algorithm to compute the Padé
> approximants at a point (in certain point). In the affirmative case, how is
> the stability of the algorithm?

Yes there is an algorithm which (fundamentally) rely on linear algebra. Its
stability depends on the underlying stability of the linear algebra routine
used.

The algorithm is implemented in PARI, but I do not expect it to be stable.

Cheers,
Bill.