It should be noted that the CPU values for TFU are not the directly 
measured ones. An improvement of the TFU program, suggested in /13/, 
was not implemented in the program used in the test, while an 
equivalent improvement was incorporated in the GT program. Thus the 
measured CPU times were not quite compatible. However, it was possible 
to isolate the time for a program sequence which would be involved by 
the improvement in the TFU program, and a part of this time was 
subtracted, based on judgement of the expected effect of the 
improvement. 
DISCUSSION AND CONCLUSIONS 
When drawing conclusions from the present data, one should keep in mind 
the limited accuracy of the values for TFU in the diagram. It should 
also be noted that the absolute values of the times are not 
representative for an operating OLT system, since the computer of an 
OLT system is not expected to be of the same size or speed as the one 
used in the test. 
The diagram indicates that, with the data set used, the GT algorithm 
works faster than the TFU algorithm when adding few new observations. 
When measuring on single photos, which is often the case in close range 
photogrammetry, this feature of GT may be advantageous. 
The fact that GT times seem hardly to increase with the number of 
unknowns, when adding two observations, could be explained by the 
extremely “nice” data sets far all the "+2" .updates. Each of these 
updates implies operation on the smallest possible part of the normals. 
This applies to TFU as well, although TFU times do increase. 
Further tests are required to clarify how the computing times depend on 
number of photos involved in an update and their positions in the 
normals. This might confirm or reduce the indicated advantage of GT. It 
might also be interesting to test whether the slight trend of better 
performance of GT with higher numbers of parameters is significant or 
not. 
GT may not compete with TFU if the updates are to be performed with 
larger groups of observations. But the time for the smaller updates 
with GT are expected to allow the update to take place between point 
readings. Thus only the back substitution is required whenever the 
parameters are to be computed. 
The GT algorithm may be further improved. The Givens transformations 
without square roots presented in /3/ would speed up the 
process. There are also potentials for efficiency improvements in the 
current program. 
As a conclusion, the test has shown that an algorithm based on Givens 
transformations is at least competitive, and in some respects 
advantageous compared to the Triangular Factor Update algorithm. 
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