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

[Jay Howard]

Actually, my question was more related to the nonlinear methods.  For
the purposes of gsl_multifit_test_delta(), how should I understand the
parameter "epsabs" ("absolute error")?  Is it RMSE (or a similar
measure) over the set of m residual errors, or something else
entirely?

On Dec 5, 2007 3:32 PM, Barrett Foat <address@hidden> wrote:
>
> 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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