4.4 Sub-Block Adjustment 
The purpose of the final adjustment is to minimize -- or 
eliminate — the discrepancies between the different values of the 
coordinates of the same point (internal agreement) and the discrepancies 
between the block coordinates and the absolute coordinates of the ground 
control points (external fit). Any procedure of adjustment will be mainly 
based on assigning a number of unknown transformation coefficients to each 
sub-block and determining the values of all the unknowns that would satisfy 
the above-mentioned conditions. There are various means to perform the 
adjustment: 
(1) by solving the entire set of condition equations in one simultaneous 
operation 
(2) by solving the entire set of condition equations, applying a 
numerical iterative procedure 
(3) by using an iterative solution for partial sets of the condition 
equations based on a relaxation method of successive approximations. 
The first method involves the simultaneous solution of an excessively large 
system of equations. This is considered, at the present time, as hardly 
practical. The second method differs from the first only in the procedure 
of solving the system of equations. It utilizes a numerical iterative 
scheme to enable the reduction of a large system of equations on a small or 
medium computer. This second method is currently under development and 
testing for the two-dimensional (horizontal) adjustment . The third 
method is based on the idea of solving for the unknowns of one sub-block at 
a time using an approach of successive approximations. It is considered in 
the following section for more detailed presentation. 
4.4.1 Adjustment by Relaxation 
The adjustment scheme is composed of the following steps: 
(1) The centroid of the coordinates of all pass points, ground control 
points, and exposure stations in one sub-block,that are common to 
adjacent sub-blocks, is computed. Thus: