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Re: Roots of polynomial equations with complex

• To: mathgroup at smc.vnet.net
• Subject: [mg92755] Re: [mg92713] Roots of polynomial equations with complex
• From: danl at wolfram.com
• Date: Sun, 12 Oct 2008 04:33:38 -0400 (EDT)
• References: <200810111044.GAA12162@smc.vnet.net>

> 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

NSolve of a univariate polynomial uses Jenkins-Traub. FindRoot only gives
one root and, depending on Method option, might use Newton or secant
methods, or Brent's method.

The development version of Mathematica has other methods for univariate
NSolve. I believe J-T will not be the default but I am not certain of
this.

Daniel Lichtblau
Wolfram Research

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