A modified-equations method for the least-squares solution of condition equations

A method is developed for the adjustment of sections of a triangulation net before the data for the total adjustment are available which does not require alteration of the sectional correlate values in order to complete the total adjustment at a later date. The computational process, using Bjerhammar's solution for normal equations, leads to sectional corrections to which are added partial corrections derived from the additional equations to obtain total corrections satisfying the expanded system. The method can also be used to advantage to complete the adjustment of an expanded system of equations, the original part of which was solved by either the Gauss-Doolittle or Cholesky techniques. Two numerical examples are appended.