Re: Leasqr matrix singular to machine precision

[Archambault Fabien]

First thank you for your answer,

Selon Francesco Potorti` <address@hidden>:

> >As I could not solve the system I was asking why and found from the
> >example leasqrdemo that I can give more points than the number of
> >unknown (an overestimated system is possible !).
>
> Sure it is possible!  That is the whole point of least square
> optimization.

That was one poin I didn't understood because before using leasqr I wanted to
use fsolve that's why I thought I needed only a square matrix.

>
> >If I try to modify the inital guess it doesn't converge and arrive to
> >imaginary values...
>
> Try with more points, and with different initial guesses.  Try with a
> simpler problem, and change it gradually.  Try to start with something
> that you know has a solution.

I tried as I explained on a 4 unknown system with 15 points this doesn't work.
As it was a "fictive" system I knew the answers so I was able to add points.
I tried on 20 and 25 points same problem.

Also when I will use the script The values of y will be given by calculations
that are very long to have so I have limited values (15 maximum for a system).

>
> >Now I need help ! Does 4 variables are too much ?
>
> Definitely not.

As I mentioned before I couldn't solve the system with 4 variables. So solving
with my 6...

Now I am trying to add the derivatives because the equation is easily derivable
and it will perhaps solve the problem for any reason the numerical derivatives
are perhaps not well calculated (it is weird to think it but I do not know).

>
> --
> Francesco Potortì (ricercatore)        Voice: +39 050 315 3058 (op.2111)
> ISTI - Area della ricerca CNR          Fax:   +39 050 315 2040
> via G. Moruzzi 1, I-56124 Pisa         Email: address@hidden
> Web: http://fly.isti.cnr.it/           Key:   fly.isti.cnr.it/public.key
>

A last thing I have a dead line for my calculations that will be soon so I have
to solve my problem with any possibility I have. That's why I am at the moment
writing something (in Fortran) to use the lmder subroutine. I think in the
morning it will be completed I will know if the difference between the
algorithm in lmder and leasqr explains my problem.

Thanks again for your answer, if someone has another clue or question I will be
glad to answer.

Fabien Archambault

-- 
Fabien Archambault
Equipe de dynamique des assemblages membranaires
Unité Mixte de Recherches CNRS UHP 7565
Université Henri-Poincaré, Nancy I BP 239,
54506 Vandoeuvre-lès-Nancy, cedex France

Tél : 03.83.68.43.96