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>