Rigorous Formulas for Effects of Weight Changes

by Mohamed F. Madkour, (M.ASCE), Aerial Surveying Division, Survey of Egypt, Presently on leave with the Survey Dept. of Libya, Tripoli, Libya,

Serial Information: Journal of the Surveying and Mapping Division, 1971, Vol. 97, Issue 2, Pg. 173-184

Document Type: Journal Paper


A simple mathematical approach, in the form of basic matrix algebra relationships, is developed and numerically tested. This approach is followed in order to obtain rigorous formulas for the correction to a precomputed solution of a least squares problem due to changes in the weight matrix of the problem. Correction formulas for the methods of indirect observations and adjustment by conditions are developed. Two numerical examples that demonstrate the rigorousness of the developed formulas are presented. The developed approach can be extended in order to cover almost all possible cases of least squares problems.

Subject Headings: Matrix (mathematics) | Least squares method | Case studies

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