[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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