# Re: [R] Roots of quadratic system.

From: Sebastian Leuzinger <Sebastian.Leuzinger_at_unibas.ch>
Date: Tue 03 May 2005 - 01:11:49 EST

Hi,
I used polyroot() and it works fine.
Sebastian

On Monday 02 May 2005 02:51, John Janmaat wrote:
> Hello Bill,
>
> I have used the optimization approach you suggest in past. I was hoping
> that someone had written something specifically for solving a system of
> nonlinear equations, as the fsolve function does in MatLab. The Octave
> version is somewhat limited compared to the MatLab version, and I like
> working in R.
>
> Thanks,
>
> John.
>
> ps: I would like the system to have a unique solution, but there is
> nothing about the system that precludes multiple equilibria. Of course,
> the L(x) = ... approach can search for multiple equilibria if I try
> enough different starting points.
>
> Bill.Venables@csiro.au wrote:
> > Are you looking for a unique solution or families of solutions?
> >
> > Can't you turn a root-finding problem for a system of equations
> > with a unique solution into an optimisation problem, anyway?
> >
> > E.g. You want to solve
> >
> > f1(x) = g1
> > f2(x) = g2
> > ...
> >
> > Why not optimise L(x) = (f1(x) - g1)^2 + (f2(x) - g2)^2 + ...
> > with respect to x? If the minimum value is zero, then you are
> > done; if it is greater than zero your original system does not
> > have a solution.
> >
> > If you are in the complex domain the changes needed are obvious.
> >
> > V.
> >
> > : -----Original Message-----
> > : From: r-help-bounces@stat.math.ethz.ch
> > : [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of John Janmaat
> > : Sent: Monday, 2 May 2005 12:48 AM
> > : To: r-help@stat.math.ethz.ch
> > : Subject: [R] Roots of quadratic system.
> > :
> > :
> > : Hello,
> > :
> > : I have a system of quadratic equations (results of a
> > : Hamiltonian optimization)
> > : which I need to find the roots for. Is there a package
> > : and/or function which
> > : will find the roots for a quadratic system? Note that I am
> > : not opimizing, but
> > : rather solving the first order conditions which come from a
> > : Hamiltonian. I am
> > : basically looking for something in R that will do the same
> > : thing as fsolve in
> > : Matlab.
> > :
> > : Thanks,
> > :
> > : John.
> > :
> > : ==============================================
> > : Dr. John Janmaat
> > : Department of Economics
> > : Tel: 902-585-1461
> > :
> > : ______________________________________________
> > : R-help@stat.math.ethz.ch mailing list
> > : https://stat.ethz.ch/mailman/listinfo/r-help
> > : http://www.R-project.org/posting-guide.html

```--
------------------------------------------------
Sebastian Leuzinger
Institute of Botany, University of Basel
Schönbeinstr. 6 CH-4056 Basel
ph    0041 (0) 61 2673511
fax   0041 (0) 61 2673504
email Sebastian.Leuzinger@unibas.ch
web   http://pages.unibas.ch/botschoen/leuzinger

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