Prof. F. Ann Walker Research Group, Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA

Optimization algorithm

If the information about experimental errors is available, then the master equation for the Least Squares Method is expressed as weighted sum of squared deviations

The weights reflect the experimental accuracy: they are chosen as an inverse variances.

At the minimum 

Substituting

for the linear parameters we have K sets of 2x2 equations

They can be resolved exactly. The minimization with respect to the energy gap is performed numerically.


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©Nikolai V. Shokhirev, F. Ann Walker, 2002