# Re: [R] Roots of quadratic system.

Date: Mon 02 May 2005 - 10:51:56 EST

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
> :
>

```--
==========================================
Dr. John Janmaat
Department of Economics