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of the normal equation system for an unlimited strip as shown in Fig. (16), 
(formula (127)), are performed with a certain scquence of matrix operations, 
formulas (22) to (30).. This technique however, is as shown by Gotthardt in 
[15] none other than the classic Gaussion elimination for two unknowns, 
applied to matrix calculus. The alternate solution for solving the system 
of normal equations of a strip or block triangulation using an iterative 
approach, 1s based on the Gauss-Seidel Relaxation method [17], in connection 
with a procedure which has proven useful in similar applications, known as 
"Smoothing with Moving Arcs." 
Consequently, the knowledge of the classical geometrical considerations 
dealing with a central projection, and a certain familiarity with the method 
of least squares adjustment, as applied in geodesy, suffice to solve the ana- 
lytical problems arising from the application of photogrammetric measuring 
systems. 
As previously mentioned, the system of normal equations (35) schematically 
shown in Fig. 4, is typical for the most general problem of analytical photo- 
grammetry. The system is readily accumulated because the corresponding obser- 
vational equations are based on the simplest geometrical model conceivable, 
expressing for any type of control point the condition of collinearity between 
control point, center of projection and image point. The problem of arriving - 
&t the most economical and feasible method of reduction in analytical photo- 
grammetry is, therefore, concerned with the process of determining the roots 
of this normal equation system. The solution presented in this report is 
based on the formation of a system of reduced normal equations (formulas (37) 
or (38)) by a rigorous mathematical method. The attractiveness of the solution 
arises from the presence of a series of separated square matrices along the 
main diagonal. This feature, however, is lost in the resulting system of 
reduced normal equations, where, quite obviously, all the remaining unknowns 
are more or less correlated, depending on the geometrical arrangement of the 
cameras. Any attempt to further simplify the process of determining the roots 
of the normal equation system (35) as it is readily seen from Fig. 4, must try 
to preserve all of the fully separated square matrices along the main diagonal 
during a complete computational cycle. Such a result is obtained if a compu- 
tational cycle, using the relaxation techniques, is established around the point 
79