       Simultaneous Nonlinear Data Fits

• To: mathgroup at smc.vnet.net
• Subject: [mg109013] Simultaneous Nonlinear Data Fits
• From: "Dan O'Brien" <danobrie at gmail.com>
• 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.

Thanks,

-DanO

```

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