Automated Formulation of Condition Equations

Least squares adjustment of a leveling network entails formulating a set of simultaneous equations, solving those equations, and calculating point elevations based on the solution. The major portion of a computational effort is exerted in solving the simultaneous equations, a task for which digital computers are effectively and widely used. Since formulating the equations and calculating point elevations are not as tedious as manually solving simultaneous equations, little emphasis has been placed on using the computer to perform those operations. Nevertheless, significant savings in manual effort can be affected by extending the domain of network adjustment programs to include generation of equations and calculation of point elevations. This note presents a compilation of existing algorithms from both adjustment theory and linear network theory, organized to be of maximum use in implementing such an extension.