[SciPy-user] transcendental root finding

Ryan Krauss ryanlists at gmail.com
Tue Nov 8 14:58:35 CST 2005


I have not tried that.  I will think about that one.  It sounds interesting.

Ryan

On 11/8/05, Nils Wagner <nwagner at mecha.uni-stuttgart.de> wrote:
> On Tue, 8 Nov 2005 15:34:06 -0500
>   Ryan Krauss <ryanlists at gmail.com> wrote:
> > Does anyone out there have a robust algorithm for
> >finding all of the
> > roots of a transcendental equation within a certain
> >range of the
> > independent variable.  I wrote one myself that takes a
> >vector of
> > guesses that are used in optimize.newton.  I am trying
> >to use this
> > algoritm as part of a root locus finding tool.  Each
> >initial guess
> > would represent a branch of the locus and I was hoping
> >to stay on the
> > branch as a gain is slowly increased.  For at least one
> >of my branches
> > this isn't going very well and newton converges to
> >another nearby
> > solution on some occassions.
> >
> > Any thoughts?
> >
> Have you tried a homotopy approach
>
> H(x,t) = (1-t) g(x) + t f(x) = 0
> t \in [0,1]
>
> f(x) is your transcendental equation
> g(x) is a simpler function with known zeros.
> You start with t=0 and increase t until t=1.
>
> For t=1 you will hopefully find a solution of f(x)=0.
>
> Nils
>
> > Ryan
> >
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