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Re: Leasqr matrix singular to machine precision

From: Archambault Fabien
Subject: Re: Leasqr matrix singular to machine precision
Date: Fri, 22 Feb 2008 14:30:49 +0100
User-agent: Thunderbird (X11/20080213)


thanks again for your answers.

Francesco Potorti` a écrit :
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.

I'll try with more guesses.  Sometimes what you really want is a fit in
the log sense, e.g., when you want to fit a line in dB scale.  In this
case, you'd better use a log of your data.  Or sometimes some of your
points are particularly noisy or for some reason not as significant as the
other ones.  You can use the wt argumetn to assign different
significance (weight) to different points.

For the weight on some points I thought of it but as the values I get are all of the same importance I think fitting with wt = (1) is a correct guess.
As I mentioned before I couldn't solve the system with 4 variables. So solving
with my 6...

While generally it is tru that more variables make the problem harder,
this is not a hard rule.  Try with 6, maybe it is better.
I will try again with 6 but I have few hope.
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).

If you do not supply a derivative function, a numerical derivation is
done.  Depending on the problem, this could lead to bad results, even if
usually this is not the case.

By the way, I am writing these suggestions not because I am an expert in
the field of nonlinear optimisation, but just because of my moderate
experience in using leasqr (and noone else more expert showing up).

That is what I understood from the "manual". Also I was able to see that the derivatives computed numerically and analytically are nearly the same.

Finally, for the moment, the subroutine lmder from minpack can converge to a guess that is physically acceptable without a lot of difficulty. So the difference between lmder and leasqr is really important.

I am still open for any modification that can be made because octave is a great tool and easy to use.

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

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