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RE: Re: LevenbergMarquardt

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86622] RE: [mg86598] Re: LevenbergMarquardt
  • From: "Ausman, Kevin" <ausman at okstate.edu>
  • Date: Sat, 15 Mar 2008 03:10:57 -0500 (EST)
  • References: <200803140918.EAA11283@smc.vnet.net>

> >The parameters for residFunc are some experimental data and some
> >fitting paramters (typically in lists), and it returns a
> >one-dimensional list of numbers.
>
> This last comment suggest you want to do a least squares fit of
> data to a specified model. While it should be possible to do
> this with FindMinimum, why not use FindFit? FindFit is
> specifically designed to solve a least squares problem while
> FindMinimum is a more general tool. As a general rule of thumb,
> tools more specifically designed for a given problem in
> Mathematica will outperform more general tools for that problem.
>
> Like FindMinimum, the default method for FindFit is Automatic.
> However, I believe FindFit tries Levenberg-Marquardt first with
> this setting since that will generally produce better results
> for a non-linear least squares problem.

I would love it if there were a way to efficiently use FindFit for my 
problem. I rejected that approach because my model includes a 
ListConvolve step, so it produces a list of {x,y} values. My 
understanding (perhaps incorrect?) of FindFit is that it requires the 
model to be in a functional form, not in an already-evaluated list form. 
So am I correct that using FindFit would require that I interpolate my 
resulting data first? That seems very inefficient since FindFit would 
just be re-evaluating that interpolated function at those very same data 
points to compare to the experimental data.

I have been fighting this particular problem for over a month now, and I 
am beginning to believe that my attempts to boil the error down to its 
essential elements are all failing. Every bit of model code that I have 
written to try to distill the problem seems to work perfectly; I am only 
having trouble with getting those simplified parts to talk to each 
other. Today I will try to write up the complete problem and will submit 
the whole thing to the group rather than little bits that I have carved 
off. I just hope that someone will be willing to dive in with me.

Thanks.

Kevin Ausman



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