Re: fsolve improvements

[Jaroslav Hajek]

On Mon, Jan 26, 2009 at 2:26 PM, Francesco Potortì <address@hidden> wrote:
>>AFAIK, leasqr is not currently part of Octave.
>
> In fact, it is part of the optim package.
>
>>If you're referring to leasqr that is part of Octave-Forge, the only
>>thing I can guess with reasonable confidence is that fsolve will have
>>superior performance per iteration, especially if the system is large
>>and jacobian not supplied (leasqr does one jacobian and one SVD per
>>iteration, vs. fsolve's one jacobian and one QR per *several*
>>iterations).
>
> Hm.  This is good and confirms my hopes.  Leasqr has lots of optional
> input and output parameters that are useful to tune the problem and
> obtain additional info, maybe you can use it as a source of inpiration.
>

Eventually, I'll look at what can be incorporated. But I think the
interface should stay mostly Matlab-compatible, so that's a
limitation. I think some of the computations in leasqr, can be done as
simple post-processing - that would be best made as a separate
function. An alternative would be to try to modify leasqr to
(optionally) use fsolve as its "core" solver, and then compute the
additional statistics. Maybe this would be the best approach.

>>Test cases would, of course, be welcome.  I'm sure there will be room
>>to improve.
>
> I have used leasqr in the past.  I hope I'll manage to reduce one of my
> computations to make a test case.  I have used few variables, but lots
> of points (i.e. vastly overdetermined systems).
>

The performance of GN-like methods for overdetermined systems
generally depend on the expected residual.
If the residual is large ("large" being vague), it is often better to
use Quasi-Newton instead of Gauss-Newton steps, i.e. to treat the
problem as general nonlinear optimization.
Since my primary aim are now square systems (for the NLWing2 package
in Octave Forge), I have not addressed the possibility of using a
hybrid QN-GN strategy if large residual is suspected, but I intend to
do it eventually, depending on how much is the function exploited for
nonlinear fitting.

regards

-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz