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## RE: [Help-gsl] Weighted Levenberg Marquardt

 From: Tom Banwell Subject: RE: [Help-gsl] Weighted Levenberg Marquardt Date: Wed, 19 Aug 2009 09:17:34 +0000

```Hi Brian,

Thanks for you reply, it sounds similar to my solution.  I found out that if I
perform Cholesky Decomposition on my covariance matrix V = LL^T, then I can
perform regular least squares on the modified state and jacobian as follows:

F~ = L^-1 F
J~ = L^-1 J

This should simply be a case of multiplying the matrices/vectors before I
return control back to the solver.

Thanks,

Tom

> Date: Wed, 19 Aug 2009 08:56:16 +0100
> Subject: Re: [Help-gsl] Weighted Levenberg Marquardt
>
> At Mon, 17 Aug 2009 09:57:33 +0000,
> Tom Banwell wrote:
> > I have solved the problem using an unweighted Least-squares but
> > would prefer to use weighted as some of my data have larger relative
> > uncertainties.  I have seen on the GSL reference manual that I can
> > perform weighted Least-Squares using a scalar, but I wanted to use
> > the full covariance matrix, Vi.
>
> We should really provided a separate correlated fitter to take care of
> the case with a full covariance matrix.
>
> It is possible to use the existing routine by factorising the
> covariance matrix to get an expression of the form (U [ y - f(x,a)])^T
> W (U [ y - f(x,a)]) and working with the transformed variables Y=U y
> and F=U f(x,a), transforming the final values back to get the desired
> result.
>
> --
> Brian Gough
> (GSL Maintainer)
>
> Support freedom by joining the FSF
> http://www.fsf.org/associate/support_freedom/join_fsf?referrer=37

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