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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 16:19:22 -0600 |
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?
> >
> >
>
> > _______________________________________________
> > Help-gsl mailing list
> > address@hidden
> > http://lists.gnu.org/mailman/listinfo/help-gsl
> >
>
- [Help-gsl] non-linear least squares fitting, Jay Howard, 2007/12/04
- Re: [Help-gsl] non-linear least squares fitting, Barrett C. Foat, 2007/12/04
- Re: [Help-gsl] non-linear least squares fitting, Jay Howard, 2007/12/04
- Re: [Help-gsl] non-linear least squares fitting, Barrett C. Foat, 2007/12/05
- Re: [Help-gsl] non-linear least squares fitting, Jay Howard, 2007/12/05
- Re: [Help-gsl] non-linear least squares fitting, Barrett Foat, 2007/12/05
- Re: [Help-gsl] non-linear least squares fitting,
Jay Howard <=
- [Help-gsl] Re: non-linear least squares fitting, Richard Henwood, 2007/12/05
- Re: [Help-gsl] Re: non-linear least squares fitting, Barrett Foat, 2007/12/05
- [Help-gsl] Re: Re: non-linear least squares fitting, Richard Henwood, 2007/12/06
- Re: [Help-gsl] Re: Re: non-linear least squares fitting, Barrett C. Foat, 2007/12/06
- Re: [Help-gsl] Re: Re: non-linear least squares fitting, Jay Howard, 2007/12/07
- Re: [Help-gsl] Re: Re: non-linear least squares fitting, Barrett C. Foat, 2007/12/10