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The BSOR approach suffered from two primary shortcomings. The 
first was that the number of iterations required for satisfactory con- 
vergence turned out to be rather sensitive to the quantity and distribution 
of absolute control throughout the block — the more control, the faster 
the convergence. With minimal or sparse control slowness of convergence 
could detract significantly from the otherwise satisfactory efficiency of 
the reduction. The second shortcoming of the BSOR approach was that it 
did not produce the inverse of the coefficient matrix of the normal 
equations. As a result, the computation of the covariance matrices of 
the triangulated coordinates could not be accomplished efficiently. 
Because of the shortcomings of the BSOR reduction the search for 
greater computational efficiency continued. The next advance occurred in 
Tate 1965 with the development at DBA of an algorithm named recursive 
partitioning. This algorithm, first published in Gyer (1967), is designed 
expressly to exploit the characteristic banded structure of the reduced 
normal equations generated by the typical aerial block with appropriately 
ordered photos. This banded structure is illustrated in Figure 3 for a 
sequence of blocks conforming to the cross-strip ordering scheme indicated 
in Figure 2. With such ordering all nonzero elements of the coefficient 
matrix are confined to a diagonal band the width of which depends only on 
the number of strips in the block (for a particular degree of side overlap) 
and is totally independent of the number of photos per strip. 
Recursive Partitioning is applicable not only to banded systems 
but also to banded-bordered systems having the structure indicated in 
Figure 4 which depicts an NxN coefficient matrix having bandwidth p and 
borderwidth q. As shall be seen in due course, the availability of the 
band in this system affords diverse opportunities for the practical 
extension of the basic bundle adjustment to accommodate the introduction 
of parameters common to significant subsets of photos. As adopted from 
Brown (1968a) a concise explanation of the process of recursive partition- 
ing proceeds as follows. One begins with the quadruply partitioned banded- 
bordered system of bandwidth p and borderwidth q indicated below, 
  
  
  
  
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