Re: global fit

• To: mathgroup at smc.vnet.net
• Subject: [mg57482] Re: [mg57435] global fit
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sun, 29 May 2005 01:03:42 -0400 (EDT)
• References: <200505280938.FAA21631@smc.vnet.net>
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```If you look in the advanced documentation for find minimum (I think it
is called unconstrained optimization), it shows how root finding
functions may not necessarily find the root nearest their starting
point. I think there are options to establish a weighted trust region
about the starting point that can help reduce the step size. Maybe

On 5/28/05, Pascal <Pascal.Plaza at ens.fr> wrote:
> Hi,
>
> Here is a fascinating problem:
>
> B is a large data matrix, typically 500x60. Each line represents the
> variations of a given physical quantity as a function of time. There
> are here 60 different times.
>
> The problem is to fit all the lines of B with a linear combination of a
> reduced number (say 5) of base functions: f1[t], f2[t]...
> If A is the 5x60 matrix A[[i,j]] = fi[tj], I have to find an X matrix
> (500x5) such that X.A is as least-squares close to B as possible.
> At this point the solution is just X = B.PseudoInverse[A]
>
> It gets more interesting when the base functions depend non-linearly on
> a few parameters: a, b, c...
> Now the problem is to find X and a, b, c... such that X.A[a,b,c...]is
> the best fit to the data matrix B.
>
> I built a function of a, b, c... returning the 2-norm of X.A-B , after
> calculating A with parameters a, b, c... and estimating X with
> B.PseudoInverse[A]
> Then I tried to use FindMinimum on this function. I entered a very good
> starting point but the Kernel rapidly uses all the memory available and
> shuts down.
>
> Does anyone has a suggestion, maybe with a completely diffrent method?
> Thanks.
> Pascal.
>
>

--
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

```

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