# [SciPy-user] transcendental root finding

Ryan Krauss ryanlists at gmail.com
Wed Nov 9 08:52:54 CST 2005

Any other ideas?

Ryan

On 11/8/05, Ryan Krauss <ryanlists at gmail.com> wrote:
> 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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