Re: data fitting

[Joe Koski]

Jiri,

This problem falls into the general area known as "parameter estimation
theory." 

A singular Jacobian matrix during the least-squares fit usually indicates
that you have two or mare parameters that are linearly dependent. You can
find which parameters are giving you trouble by plotting (versus x) the
normalized sensitivity coefficients (for example, for a1, the normalized
coefficient would be a1 times the partial derivative of y with respect to
a1). With octave as a tool, you can plot all the sensitivity coefficients
for a1, a2, a3, and a4 on the same plot versus x. If you see the same shape
for two or more curves, then there's the problem, and you have to find an
independent way to get one of the parameters. You will also see over which
ranges of x the various parameters are important, and which parameter has
the highest relative sensitivity.

There are some text books on the subject out there. The course that I took
long ago used Beck and Arnold, "Parameter Estimation in Engineering and
Science," but it is long out of print, and not very easy to follow.

Joe


on 2/21/05 10:08 AM, Jiri Pachman at address@hidden wrote:

> Hi all,
> I am trying to determine parameters of equation by fitting it to
> experimental data. The equation is in the form of:
> 
> y = a1 * (x*a2)/(1+x^2*a2^2) + a3 * (x*a4)/(1+x^2*a4^2) + ....
> 
> a1, a2, a3 etc are the parameters I am trying to find. I started with one
> (a1, a2) and went up to make sure I am not too far with the initial guess.
> I used leasqr and it was ok on theoretical data, but when I try to use it
> on real ones it fails. I get inverse matrix singular to machine precision.
> I found in literature (since this is typical problem from rheology) that
> this kind of problem is ill-posed in its nature and is solved by using
> Thikonov regularization. I just wanted to know, if there is a more robust
> way in octave to fit the data.
> 
> thanks
> 
> Jiri
> 




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