[Date Index]
[Thread Index]
[Author Index]
Re: Roots of polynomial equations with complex coefficients
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92742] Re: [mg92713] Roots of polynomial equations with complex coefficients
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Sun, 12 Oct 2008 04:31:16 -0400 (EDT)
*References*: <200810111044.GAA12162@smc.vnet.net>
For a single univariate polynomial NSolve uses the Jenkins-Traub
method. I don't know what you can mean by a "very complicated
polynomial equation", though. Polynomials differ by their degree and
by whether they are dense or sparse. So presumably you mean a dense
polynomial of a high degree? One alternative to the Jenkins-Traub is a
version of the method NSolve uses to deal with systems of polynomial
equations: you set up the companion matrix and compute its
eigenvalues. Of course you need a good eigenvalue finding algorithm.
There are many of these (the power method, QR, LR) and others - I am
not sure which one Mathematica uses by default.
I don't think you can see the C-code behind NSolve - Mathematica is
not open software.
Andrzej Kozlowski
On 11 Oct 2008, at 19:44, Luiz Melo wrote:
> HI MathGroup,
>
> Does anybody know the algorithm Mathematica uses when NSolve is
> dealing with
> polynomial equations with complex coefficients? Is it the Jenkins-
> Traub method?
> I'm willing to write a Fortran code to compute polynomial roots of a
> very
> complicated equation that Mathematica apparently cannot handle with
> NSolve or
> FindRoot. I ultimately would like to see the C code behind NSolve,
> but I wonder
> it is kept as a secret by Wolfram.
>
> Thanks,
> Luiz
>
>
>
> --
>
>
Prev by Date:
**Re: FindFit**
Next by Date:
**Re: FindFit**
Previous by thread:
**Re: Roots of polynomial equations with complex**
Next by thread:
** Re: Roots of polynomial equations with complex coefficients**
| |