[Numpy-discussion] roots and high-order polynomial

[Nils Wagner]

On Fri, 03 Jul 2009 11:48:45 +0200
  Fabrice Silva <silva at lma.cnrs-mrs.fr> wrote:
> Hello
> Has anyone looked at the behaviour of the (polynomial) 
>roots function
> for high-order polynomials ? I have an application which 
>internally
> searches for the roots of a polynomial. It works nicely 
>for order less
> than 20, and then has an erratic behaviour for upper 
>values...
> 
You will need multiprecision arithmetic in that case.
It's an ill-conditioned problem.

> I looked into the source and I wondered that roots is 
>based on the
> eigenvalues of the companion matrix. For high-order, 
>this latter is
> rather sparse. Would it improve anything to compute the 
>eigenvalues
> using sparse solvers?

No.
  
Cheers,
                        Nils