7.2 Irregular boundary 
The irregular boundary of the photographed area, or 
the existence of lakes or large water bonds, or the 
intentional extension of one strip, or more, to 
cover a ground control point outside the boundary, 
or any other reason might give rise to a situation 
whereby the numbers of models in adjacent strips 
are not the same, and/or the starting models in 
them might not coincide. The change in M would 
take place in the structure of the correlation 
submatrix b(k, k+1). The key to define this 
structure is to find the order of the first and 
last models (0) in a line L(k) and the order of 
the joined with them first and last models (B,Y) in 
the following line L(k+1); and the number of models 
joined with each. It should be noted that 0 and/or 
DB is the first model in its line, also Ww and/or Y 
is the last. The order of these models (d,B), 
(W,Y) gives the start and end non-zero basic 
covariance matrix m of one diagonal (if they fall 
on one diagonal) or two boundary diagonals 
respectively (if they fall on different diagonals). 
The number and location of non-zero diagonals of 
b(k,k+1) are then identified as in the two 
illustrated cases by figure 15. 
The resulting pattern of M for any combination of 
irregularities with different p$, q$ could be 
constructed by integrating the appropriate basic 
concepts. 
7.3 Irregular scale and orientation of photography 
The irregular scale and/or orientation of photo- 
graphy could arise when different date photography 
are used for aerial triangulation. This might 
result in a model being connected with several 
other models by varying numbers of tie points. In 
this case a search routine should be employed 
(Julia, 86) to identify the points common to 
particular models, and which models are connected 
by one and the same point. The minimum bandwidth 
strategy for ordering the models might be suitable 
for this situation. 
8. CONCLUSION 
The established patterns of M and the numerical 
examples make it possible to conclude the following 
remarks and recommendations: 
(1) The sparsity and structure of the coefficient 
matrix M has the property of regular band pattern, 
where the non-zero basic matrices m lie within a 
diagonal band W. The decomposition of M can be 
performed within this band. 
(2) The storage of the matrix M is most suitably 
accomplished by diagonal storage. The storage space 
of the non-zero envelop is the most economical. 
This storage system is most suitable for solution 
by Gauss elimination. 
(3) The storage of M with its full half bandwidth 
W would require extra storage facilities from 5%- 
25%, 
(4) If the solution is sought by partitioning, the 
best candidate for a partitioned unit is the sub- 
matrix b. The half bandwidth of M in this case is 
D, with 25$-70$ additional storage requirement. 
(5) The ordering of the models has a prime influence 
on the size of M. The number of F.I. « s? g? for 
ordering across - strip, down-strip respectively. 
(6) The conditions for economical ordering depend 
on p$,q$,8 and g..These conditions could be set in 
the computer program to resequence the models. 
Together with a suitable computer graphics facility 
manipulation of the ordering for least size of M 
could be achieved. 
249 
(7) The rise in the p$, q$ increases the number of 
models. The increase is almost linear with every 
20% step increment of p & gq (g=20% = g=40%). 
(8) The inclusion of the corss models, if they are 
possible to be constructed, almost doubles the 
number of the constructed models and quadrable the 
size of M. 
(9) The inclusion of the cross models is antici- 
pated to strengthen the solution. The significance 
of the improvement yet to be established versus the 
cost of additional observations and increase in 
storage and computation time. In this case the 
economy in storage and computation of M composed of 
models' transofrmation parameters against coordi- 
nates of the points should be investigated. 
(10) For very large M,perdherals are recommended to 
be used with micro computers to transfer to and 
from the core the active part of M necessary for 
forward reduction or back substitution of one step 
at a time. 
9. REFERENCES 
(1) Cuthill, E., 1972. Several strategies for 
reducing the bandwidth of matrices. In: D.J.Rose 
and R.A. Willoughby (Eds.), Sparce Matrices and 
Their Applications. Plenum Press, New York, 
pp. 157-166. 
(2) Jennings, A., 1977 Matrix Computations for 
Engineers and Scientists, John Wiley & Sons, 
London, pp.145-181. 
(3) Julia, J.E., 1984. A general rigorous method 
for block adjustment with models in mini and micro 
computers. In: Int. Arch. Photogramm. Remote 
Sensing., Rio De Janiero - Brazil. Vol. III, Part A 
3a, pp.473-480. 
(4) Julia, J.E., 1986. Development with the COBLO 
block adjustment program.  Photogrammetric Record 
12(68): 219-226. 
(5) Klein, H., 1988. Block adjustment on personal 
computers. In: Int. Arch. Photogramm. Remote 
Sensing., Kyoto - Japan. Vol. 27, Part B-11, 
pp. 111 588 = ITT 598. 
(6) Kruck. E., 1984. Ordering and solution of 
large normal equation systems for simultaneous 
geodetic and photogrammetric adjustment. In: Int. 
Arch. Photogramm. Remote Sensing., Rio De Janeiro- 
Brazil, Vol. III, Part A-3a, pp. 578-589. 
(7) Lukas, J.R., 1984. Photogrammetric densifica- 
tion of control in Ada County, Idaho: data 
processing and results. Photogrammetric Engineer- 
ing and Remote Sensing, 50(5): 569-575. 
(8) shan, J., 1988. On the optimal sorting in 
combined bundle adjustment. In: Int. Arch. 
Photogramm. Remote Sensing., Kyoto-Japan. Vol.27, 
Part B-3, pp.744-754. 
(9) Stark, W., Steidler, F., 1983. Sparce matrix 
algorithms applied to DEM generation. Bulletin 
Geodesique, 57(1):43-61. 
(10) Wang, K.W. 1980. Manual of Photogrammetry, 
Fourth Edition. American Society of Photogrammetry, 
Va., pp.94-96. 
Errata to Table 1 
Ordering (282) for p-80$, q-60$, (4C) 
D W E.I. 
5(2s-1) 8s-2 (139-37) (s-2) (s-3) 
(782) +(g-6)s(2s-1) 
£0.59; 87+ (25/s)