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From: "Bruno Luong" <b.luong@fogale.fr>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Is this kind of regression possible?
Date: Wed, 2 Jan 2008 22:59:29 +0000 (UTC)
Organization: FOGALE nanotech
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"vicky " <vivek_mutalik@yahoo.com> wrote in message
<flfcpq$nf8$1@fred.mathworks.com>...
>  
> For following equation:
> 
>  [8 - (W1A + W2C + W3A + W4G)]^2 + [10 - (W1A + W2T + W3T
>  +W4C)]^2 + and so on.
> 
> Can i give initial guess for W1A, W2C, W2T, W3A,W3T,W4C and
> W4G and solve this equation to obtain their values after
> minimizing the residual sum of square ? 
> 

Yes! As I wrote above the following:

[ In the case of overdetermined linear system, using pinv()
is a better choice, because W=pinv(M)*Y is well defined.
It's the unique solution that verifies the two following
conditions:

(i) M*W = Y
(ii) |W| is minimum among all W that satisfied (i). ]

Gradient minimization algorithm - without preconditioning -
when fully converged, provides the solution (among the set
of solutions) which minimizes the L2^norm to the first-guess.

The algebric solution W=pinv(M)*Y is what one obtains with a
gradient algorithm starting from 0 as first-guess.

If you want an equivalent algebric solution to a
minimization from a first guess W0, do the following:

W = W0 + pinv(M)*(Y-M*W0)

Bruno