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

From: Jay Howard
Subject: Re: [Help-gsl] non-linear least squares fitting
Date: Wed, 5 Dec 2007 13:56:33 -0600

> 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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