[Help-gsl] multidimensional root finding

[Brian Powell]

Hello -

I am trying to solve a system of nonlinear equations.  For several initial
guesses of the root, the solver (both hybrid and newton) did not converge.
 I was, however, able to obtain a solution using Maple's numerical solver.
 Armed with this knowledge, I can obtain this root with the GSL routines
if my initial "guess" is very close to the actual root.

It's a 5D system and the root is located at
{3.080,0.350,-0.159,0.126,-0.063}.
An initial guess of {3,0.2,-0.5,0.2,-0.05} finds the root, whereas a guess
of {1,0.8,-1,0.5,-0.5} does not.  Is this normal behavior?  I'm sure this
depends on the form of the equations.  Are there any ways to improve an
initial guess' chance of success, or is it perhaps necessary to try many
initial guesses until one takes?

Thank you for your help,
Brian