# [SciPy-user] transcendental root finding

Nils Wagner nwagner at mecha.uni-stuttgart.de
Tue Nov 8 14:45:50 CST 2005

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]

g(x) is a simpler function with known zeros.

For t=1 you will hopefully find a solution of f(x)=0.

Nils

> Ryan
>
> _______________________________________________
> SciPy-user mailing list
> SciPy-user at scipy.net
> http://www.scipy.net/mailman/listinfo/scipy-user