The system of equations has: 
variables = 1272 equations = 3837 
The graph has 231 nodes and 458 edges 
(figure 2). 
The following two matrices refer, 
respectively, to the end of the second (on 
the left) and third step (on the right) of 
the procedures described in the first 
paragraph to structure the matrix of the 
linearized system of equations; the number 
of the sets Kj is “forty-two (r=42). 
Reconstruction is in scale and so figure 
11 represents the real dimensions of the 
blocks within the matrix. Below the first 
dot line, in the second level, blad blocks 
are visible. They are few and can be 
eliminated shifting on the right some 
nodes to ensure the compatibility of the 
block location. The effect of this process 
  
  
  
  
  
is the increment of the block dimension of 
the last level, also visible in the figure 
11. 
The assumption of equi-dimension of blocks 
used to compute the cost is not completely 
true, expecially for the last levels. 
Since these blocks are very sparse a 
compact techinique for storing not null 
elements can enormeously reduce the cost 
of their update (up to now the cost is 
evaluated assuming that the block products 
are implemented without taking advantage 
of the sparsity). Furthermore, as there 
exists algorithms CIob, 1991) which 
produce r-42 blocks and 4/n-41141232, one 
assumption is verified in defect and the 
other in excess; consequently, the 
conjecture r-4n is acceptable. Then, in 
the graphic of the figure 10, the cost 
function corresponds to the lowest one. 
  
  
  
  
  
Y Figure 11 
| 
Bibliography - George A., Liu J.W. 1981. Computer 
Solution of Large Sparse Positive Definite 
- Benciolini B., Mussio L. 1984. System, Prentice-Hall Inc, Enflewood 
"Algoritmi di riordino delle incognite 
nelle compensazioni ai minimi quadrati", 
Ricerche di  Geodesia e  Topografia e 
Fotogrammetria, CLUP Milano. 
- # Bunch J.R., Rose D.J. 1976. Sparse 
Matrix Computation, Academic Press Inc, 
New York, San Francisco, London. 
- Forlani G., Mussio L. 1994. "Il calcolo 
di una compensazione minimi quadrati", 
Ricerche di  Geodesia e  Topografia e 
Fotogrammetria, CLUP Milano. 
108 
Cliff, New Jersey. 
- Golub G.H., Plemmons R.J. 1981. "Large- 
scale geodetic least-squares adjustment by 
dissection and orthogonal decomposition", 
Large Scale Matrix Problems, North 
Holland, New York. Oxford. 
- Iob I. 1991, "Un' alternativa al metodo 
della ‘'dissection' per la soluzione di 
grandi sistemi lineari sparsi e 
sovradeterminati", graduation thesis in 
Informatic Science, University of Udine. 
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