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nonlinear curve fitting

• To: mathgroup at smc.vnet.net
• Subject: [mg51942] nonlinear curve fitting
• From: db at ict.fhg.de (julia)
• Date: Fri, 5 Nov 2004 02:18:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

i want to use Mathematica for the interpretation of some input-rsponse
measurements. I'm a real newbie and i'm not sure how to do it and
whether
it is possible. After some first trials, there are some problems and i
hope somebody can help me.

I'm measuring an time-dependent input- and an output-signal. The input
has to
 be convoluted with a model and this convoluted product fitted to the
measured response-curve.

I've tried the build-in NonLinearFit-tool, but it didn't work well. I
think i can't use it because i have some more steps (convolution,
normalization...) to do except of just fitting a dataset to a model.
It would be necessary to combine all this steps to "model" in
"NonlinearFit[data,  model,  variables,  parameters]". I'm not sure,
if this would work....

Therefore i think i have too write an algorithm for the fit instead of
using the build-in. I've mentioned before that i don't have much
experience in programming and therefore i searched for some codes in
the web. I've taken the algorithm for a gaussian fit written by Eric
W. Weistein (which can be found here:
http://mathworld.wolfram.com/NonlinearLeastSquaresFitting.html) and
I've modified it, in order to use my models. Now I have two problems:

1. I get complex values for my model-parameters. That's cumbersome but
not really bad, because the imaginary parts are small and can be
chopped.

2. I get a negative value (even with a very good initial assumption)
for one parameter, which is physically nonsense. Does anybody know how
to bar mathematica from doing this?

I hope somebody can help me with this! Is it the right way to code it
by myself or should i better use the build-in function? Writing it by
myself would be very difficult and time-consuming. Therefore I'm
wondering why there are not more different algorithms (e.g. Rosenbrock
or other optimization algorithms) written in mathematica-code found on
the web. Does anybody know a source?

Thanks in advance

julia