The significance of Lagrange multipliers in cross-section adjustment

Describes the natural derivation of the explicit prescriptions incorporated in least-squares adjustment codes. The authors examine the central role of the Lagrange multipliers, when adjustment of cross sections by integral data is treated for what it truly is; namely, a conditional-minimum problem. The evaluation of the Lagrange multipliers necessitates the inversion only of a `small' matrix, the order of which is the number of integral data by which the cross sections are adjusted. The complete solution of the adjustment problem, i.e. the adjusted differential and integral parameters and their respective uncertainty (variance-covariance) matrices, is then given in terms of the Lagrange multipliers by simple expressions, involving no additional matrix inversions.