Re: Curve Fitting Problem ...

Modell <webgeld@xxxxxxxx> wrote in message
<623e66cc-0e53-4c58-ba65-8ca669fdfe55@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>...
Hi again mira :-)

Thanks a lot for any arguments and answers up to now !!

Still I have some trouble with the understanding of your
last hint:

1.) What is the meaning/use in "simple words" of : p(k),
k=3D 1,2,3,4
2.) I am now searching for an "Sensitivity function", and
an way how i
could minimize the sensitivity function.
Theoretical shouldn=B4t it be like that, that with
such an function
I could get an parameter set witch is the best one? How to do?
3.) One more very big problem is for me how to use the
levenberg-
marquardt for a lot of nonlinear differential equations
witch are
conntected over the process rates (chemical processes).
How is the
best way or is it in general possible to use here this l-m
algorithm ?
Or is it better to use an different algorithm?

Thanks again for any hint :-)

Paul

Hi Paul
Excuse me that I am answerin late. I was off, without any
approach to any net. To your questions:

ad 1) The written sequence in question should be read as
p(k) for k=1 or 2 or 3 or 4
ad 2) If you have a formula for a sensitivity function wit
some unknown parameters, you may continue in similar way
like with your original equations.
ad 3) Levenberg-Marquardt method is good for solution of a
set of >>algebraic<< equations. Now you are speakinq about
"nonlinear differential equations". However that is quite
another problem. I can imagine that you are trying to find
parameters of some mathematical model described by nonlinear
differential equations and you have also results of
measurements taken from a real process. Of cours, you may
apply the LM method for minimizing sum of squares of
residuals as differences between output of the mathematical
model and a real world by a modification of the model's
parameters. However it is an algebraic process irrespective
of the description of the mathematical model by differential
equations. Only to find outputs from the model will take
more time to calculate. Hence, the efficiency of a LM
algorithm is very important.

Mira



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