Roots of quadratic system.

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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