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Re: [Help-gsl] SV Decomposition.

From: Brian Gough
Subject: Re: [Help-gsl] SV Decomposition.
Date: Sun, 22 Feb 2004 19:26:13 +0000

Nomesh Bolia writes:
 > I am using SV Decomposition to solve a least squares problem. Regarding 
 > the same, I have two queries:
 > 1> In solving y = Xr (notations, as per the GSL reference manual), how do 
 > I go about solving if X has only one column. 

Currently the SVD does not handle the case of N=1, so you have to make
it a special case (or submit a patch to linalg/svd.c).

 > 2> To implement a non-negative least squares (least squares with
 > constraints of non-negativity on all solution component) routine, I need
 > to solve the ordinary least squares (y = Xr) when there are 1 or more than
 > one (Upto K-1 where K = no of columns in X) columns taking a value zero.
 > As is clear, this problem would not have a unique solution (since X'*X is 
 > singular). But, would the solution given by the gsl_multifit routine be 
 > correct under all circumstances? Or would there some issues which need to 
 > be taken care before passing on such an X as argument to the gsl_multifit 
 > function.

The source is availble in multifit/ directory if you need to see the
algorithm.  I'm not familiar with the properties of non-negative
least-squares algorithms, but if it's a self-contained problem it's
something that could be included in GSL.

Brian Gough

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