On Fri, 03 Jul 2009 11:48:45 +0200
Fabrice Silva <[email protected]> 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
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