Hi,

`I'm a computer scientist, not a mathematician and had a question
``about the Levenberg Marquardt (LM) algorithm and hoped someone would
``be able to help or provide some advice. I wanted to perform
``weighted Least-Squares and I have the following equation:
`
[ yi - f(xi,a)]^T Vi [ yi - f(xi,a)]

`where yi is the dependent variable, xi is the independent variable,
``a are the model parameters to be estimated, and Vi is a covariance
``matrix.
`

`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. I did think about using the trace
``or determinant of Vi, but not sure if that is mathematically as
``sound so wanted to use Vi. My problem is that I can't work out how
``to extend my code to include the matrix weight (rather than the
``scalar weight) and wondered if I needed to modify the internal gsl
``LM algorithm (or maybe rewrite the algorithm myself) or can apply I
``apply a matrix weight using the existing gsl LM.
`

`I hope someone can help with this, my email is: tombanwell * at *
``hotmail * dot * com
`
Thanks
Tom
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