[R] Roots of quadratic system.

[John Janmaat]

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 at 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 at stat.math.ethz.ch 
> : [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of John Janmaat
> : Sent: Monday, 2 May 2005 12:48 AM
> : To: r-help at 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
> : Acadia University
> : Tel: 902-585-1461
> : 
> : ______________________________________________
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> : 
> 


-- 
==========================================
Dr. John Janmaat
Department of Economics
Acadia University
Wolfville, Nova Scotia, Canada.