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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. *
Hello,
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.
regards
--
Brian Gough