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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
>
>
>
> --
>
>

• References:
  • Roots of polynomial equations with complex coefficients
    • From: Luiz Melo <luiz.melo@polymtl.ca>