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Re: [Help-gsl] non-linear least squares fitting

From: Barrett Foat
Subject: Re: [Help-gsl] non-linear least squares fitting
Date: Wed, 5 Dec 2007 15:32:04 -0600 (CST)

I am not as familiar with the Simplex method (so correct me if I'm wrong), but I think the "size" of the simplex is internal to the method and not directly related to the RMSE for your equation. You are probably going to need to read up on the method to see what exactly it means or tinker with the size threshold to give a final RMSE you are happy with. You, of course, do not need to use the simplex size criterion. You could stop using some criterion you devise based on the RMSE, number of iterations you will allow, or whatever.

Barrett Foat

On Wed, 5 Dec 2007, Jay Howard wrote:

The L-M algorithm requires first partial derivatives, and no other
algorithm is available in the generalized least-squares part of GSL.

Yep.  Shame on me for not RTFM, but the page labeled "Minimization
Algorithms without Derivatives" clearly explains that there are no
derivative-less solvers available at this time.  What confused me was
that there is a framework in place for derivative-less solvers, but no
solvers to go with the framework.  For instance, the method
gsl_multifit_fsolver_alloc() exists.

derivatives, you might want to consider using the GSL implementation of
the Simplex method:

Interesting.  That seems much better suited to my original line of
thinking.  I may try both.

One more question: In looking over the "Search Stopping Parameters"
page, I'm not entirely clear about the values
gsl_multifit_test_delta() accepts (epsabs and epsrel).  If after j
iterations my system is:

F_1(a_j, b_j, c_j) = error_1_j
F_i(a_j, b_j, c_j) = error_i_j
F_m(a_j, b_j, c_j) = error_m_j

Then after the next iteration it will be:

F_1(a_k, b_k, c_k) = error_1_k
F_i(a_k, b_k, c_k) = error_i_k
F_m(a_k, b_k, c_k) = error_m_k

where k = j + 1, each parameter (a,b,c) has been perturbed slightly in
the direction of the best-fit solution.

What I'm interested in minimizing is the root mean squared error of
the set of m error values.  Is that what the docs refer to when they
use the term "absolute error", or is it some other measure?

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