[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]

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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