Re: Leasqr matrix singular to machine precision

[Francesco Potorti`]

>> >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.

Mmh.  15 points could be less of what you need with 4 variables.  That
could be a problem, but I am making a guess, maybe the problem is not here.

>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.

>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).

I see.

>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.

>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).

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