Re: [Help-gsl] multidimensional root finding

[Brian Gough]

At Tue, 31 Jul 2007 17:34:44 -0400 (EDT),
Brian Powell wrote:
> 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?

Generally the approach is to scale the problem to make the root easier
to find from any direction.  Have you used the automatically scaled
version of hybrid with derivatives?  (hybridsj) That is the best
option.  Also, make sure the derivatives in the jacobian are correct -
that is a common cause of bad convergence.

-- 
Brian Gough

Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/