The flow of information in constrained least-squares fitting of experimental data

The theory of the least-squares analysis of experimental data is derived for the case where equations of constraint exist. Both the Lagrange-multiplier method and the elimination method are discussed. The covariance matrix for the parameters is derived and its properties are elucidated. Finally, the flow-of-information matrix is developed for the constrained case, and the properties of the influence and significance of the data on the parameters is derived and the differences between the constrained and unconstrained cases are discussed.