— the upper row has the same number as the lower plus one; 
- the upper row has same number or less than the lower. 
In the first case the position of the elements is immediately known: 
they are on the same columns as on lower row, but for the nearest to 
the main diagonal (fig.2.1). s 
In the second case the disposition of the non-zero elements of the upper 
row, apart from the nearest to the main diagonal, "is contained" in 
the disposition of the non-zero elements of the lower diagonal (fíig.2.2). 
Note that the total number of test is proportional to n multiplied by 
a factor much smaller than n. This remark solves completely the 
computation of the diagonal elements and of the part A of the off-diago 
nal elements. 
For the part B it is to observe that they can be accumulated separately 
while performing the operations for the part A. In this way no extra 
tests are necessary. Figure 2.3 shows the two ways to each element (i,j). 
3. EXPERIMENTS ON NETWORK AND BLOCK ADJUSTMENTS 
The experiments on network and block adjustments carried out recently 
have shown that the program CALGE works with excellent performance for 
real examples of about 10% equations and 5.103 unknowns (the library 
of the Institute does not contain bigger examples). 
The results of the experiments of adjustment are shown in Table 3.1. The 
analysis of the table allows for the following remarks. 
- The flexibility of the input format is Very high, it allows for ev- 
ery kindof surveying and photogrammetric data. Note that the identi- 
fication of a network and/or a block with a graph, i.e. the 
interpretation of connections and vertices as sides and edges, 18 
always essential. Therefore no reduction of observation equations and 
unknown parameters is performed; additional constraints are used in 
the special cases to express suitable links between unknown parameters. 
This large capability does not produce a degrade in performance of 
the program. The computing times necessary to read the observations 
and the preliminary values of the parameters, to calculate the 
coefficients, the known terms and the weights and to write the adjusted 
parameters, the residuals and their standard deviations are negligible. 
- The analysis of the computing times has shown that the most expensive 
Operation was always the inversion The investigation of this fact, 
particularly comparing the time of the inversion with the time of the 
Cholesky factorization, hassugoested to modified the inversion routine, 
as above shown. 
The gain obtained with the new version of the inversion routine is 
always 1/3 of the computing time of the old version of the same 
routine. The goal of a 2 to 1 ratio between inversion and Cholesky 
factorization is attained if the fill-in coefficient is high and, 
under this condition, if the dimension is high too: i.e. for large 
sparse matrices. 
4. TEST ON JOINT-ADJUSTMENT OF GEODETIC AND PHOTOGRAMMETRIC DATA 
Two examples on jointeadjustment are performed; the first uses italian 
data collected for a technical map; the second uses the data of the 
joint-adjustment Test of the Commission A OEEPE. 
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