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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: 3d surface fitting
Date: Mon, 28 Apr 2008 01:07:02 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Arjun Chennu" <arjun.chennu@gmail.com> wrote in message 
<fv29eq$38p$1@fred.mathworks.com>...
> > Modeling is a sometimes tricky thing, as you
> > are finding. It sounds like your data has some
> > problems. Why does data always come out that
> > way? ;-)
> 
> I don't know, but there should be a statistical law about
> the errors of experimentation.... as oppossed to just "being
> careful". :)
> 
> I'm really thankful for your (yet another) tip about
> fminspleas. Reducing it to a 3 NLP fit already starting
> giving me the right bessel form, but still couldn't do it
> well for half the datasets.
> 
> After that I used the built-in weighting options to focus
> mainly on the central lobe, and now the fits work for
> (almost) all the datasets! :-)

(Great!)

 
> I'm not sure I really understand though what fminspleas does
> different from lsqcurvefit. They both seem to solve problems
> in a least square sense, but the main difference seems to be
> in the way the parameters are handled/prioritized. 
> 
> However, I couldn't really understand why it is faster or
> more effective?

lsqcurvefit must search a parameter space of
five dimensions on your problem.

When fminspleas does the optimization, it
breaks the problem into two different classes
of parameters. Two of the parameters can be
estimated using a simple linear regression,
so fminspleas does not need to iterate over
that portion of the parameter space. These
are the "linear" parameters. In fact, a better
description is "conditionally linear". The
reduction of the problem dimensionality from
five to three dimensions is far more significant
than is the fact that fminsearch is not really a
terribly efficient optimizer.

John