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Simultaneous Nonlinear Data Fits

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  • Subject: [mg109013] Simultaneous Nonlinear Data Fits
  • From: "Dan O'Brien" <danobrie at>
  • Date: Sat, 10 Apr 2010 06:54:01 -0400 (EDT)

Hello everyone,

A small statement of my problem:  I have 4 data sets consisting of 
spectroscopic data (intensity vs frequency data).  The data contain 
resonant peaks that are fit with the modulus squared of a sum of complex 
functions (one for each peak for a total of 6 peaks) and is such that I 
must use nonlinear fitting algorithms.  Within the four data sets there 
are peaks that should be fit to the same parameters and then there are 
peaks that vary slightly from data set to data set.

The bottom line is this: I am looking for a solution of the form of a 
nonlinear fitting function that is capable of simultaneously fitting 
multiple data sets where some parameters apply to all the data sets and 
others are specific to only one of the data sets.

I have tried fitting each data set independently using the mathematica 
function NonlinearModelFit but the model is such that the 
bestfitparameters can vary wildly from data set to data set.  Using the 
option to constrain leads to computations that never end.  It would be 
best, in my mind, if Mathematica's fitting algorithm was constrained by 
having to minimize the function of the residuals when forced to consider 
all data sets at once.

I am relatively new to mathematica (I have been hacking at it for about 
a year or so) and appreciate any help this group can offer.



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