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[Help-gsl] Understanding 'ftol' in nonlinear-least-squares fitter

From: Spencer Fleming
Subject: [Help-gsl] Understanding 'ftol' in nonlinear-least-squares fitter
Date: Fri, 4 Oct 2019 12:51:00 -0600


I'm an undergraduate research student working at Boise State University.
Keeping things brief, my job is to work on a project that aims to use the
GNU Scientific Library to fit a large amount of data for scientific

We are using the gsl_multifit_nlinear module to fit each individual unit of
data. There are three coefficients it uses that are of interest to me
currently: xtol, ftol and gtol.

To my knowledge, each of these are used in a separate calculation for
error, each of which answer a different question about how close our
current guess is to the actual data.

To make things a little simpler, let's say the theoretical, ideal function
for the data we are fitting is named f(x), and the function we are
generating to approximate it is named g(x).

- xtol roughly answers "How close are we to the original guess? Did we
wander too far?"
- gtol roughly answers "For every data point x, how close is f(x) to g(x)?"
- ftol I'm not as certain about. I was hoping I could be provided with some
insight on this coefficient.

Also, I apologize if my vocabulary is a bit confusing here; as a Computer
Science major, a lot of this is new to me. However, don't shy away from
giving me a complex answer if that's what it takes to understand ftol, or
anything about the fitter. I can decipher it with a textbook and some grit!

Thank you for your time!

-Spencer Fleming

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