fsolve improvements

[Carlo de Falco]

On 26/gen/09, at 10:53, Jaroslav Hajek wrote:

> hello,
>
> I have probably finished all the fsolve improvements I intended to do
> for 3.2. I intend to do some extensive testing in the weeks to come,
> so changes may yet
> be made, but the theory is all there.
>
> Here's a summary for users interested in solving systems of  
> nonlinear equations:
>
> fsolve is now an m-file function, the old minpack code is gone. thus,
> fsolve can now be called recursively, and will automatically compute
> in single precision if given single-precision inputs. General
> rectangular systems should now be supported, solved in least-squares /
> minimum-norm sense. The interface and options supported via the
> optimset are mostly matlab-compatible, as well as the return values
> (where applicable).
> Essentially the same method as in minpack is used - double dogleg
> trust region steps with Broyden updating of the jacobian. For large
> enough (no. of variables > 10) square and overdetermined(!) systems,
> the QR factorization of the jacobian is updated rather than the
> jacobian itself, avoiding costly re-factorizations. Broyden updating
> may be switched off by the user, yielding plain levenberg-marquardt
> method.
> To fully benefit from the efficient updating, you should link Octave
> with the qrupdate library.
>
> In particular, fsolve should now be capable of general nonlinear
> fitting with expected small residuals (see the last test of fsolve).
> I encourage users to test the new fsolve and report
> problems/suggestions to this list.
>
> cheers

Hi,
Thanks for the great job!
I was wondering, does fsolve get any benefit is the jacobian is sparse?
I'm using 3.0 at the moment but I would have a few nice applications  
with nonlinear PDEs that could be interesting tests for fsolve, so I'd  
be tempted to switch to the development sources if
sparse jacobians are handled.
Carlo