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 _________________________________________________________________ Celebrate a decade of Messenger with free winks, emoticons, display pics, and more. http://clk.atdmt.com/UKM/go/157562755/direct/01/_______________________________________________ Help-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-gsl
