[Help-gsl] non-linear least squares fitting

[Jay Howard]

I have a couple of questions about GSL's non-linear least squares
functions.   Apologies in advance if they're particularly dumb
questions; I freely admit that I'm working at the edge of my expertise
here.

First:

The online docs describe two methods, gsl_multifit_fsolver_alloc() and
gsl_multifit_fdfsolver_alloc(), that are used to allocate new solvers.
 They accept a gsl_multifit_fsolver_type and
gsl_multifit_fdfsolver_type respectively.  When I examine the header
file gsl_multifit_nlin.h, I notice that it declares two solver types
of the second form (gsl_multifit_fdfsolver_lmder and
gsl_multifit_fdfsolver_lmsder) but none of the first form.  One
appears to have been available once upon a time
(gsl_multifit_fsolver_gradient) but but in my header file it's
commented out.

As the caller, am I expected to define my own gs_multifit_fsolver_type
to pass to gsl_multifit_fsolver_alloc()?

Second:

The fdfsolver docs state that the number of observations (n) must
equal or exceed the number of parameters (p).  For my project, I only
have one function/observation, F(X1, ..., Xp), that I'm attempting to
minimize.  For the purposes of using the LM functions, would it
suffice to just duplicate this function/observation p times, so that
the (n >= p) requirement is satisfied?  This would be the special case
where F1 = F2 = ... = Fn with (n = p).

Thanks in advance.