Two possibilities for the solution of. this problem shall be discussed, 
The first solution is rigorous. Its result is influenced only by the 
propagation of the rounding errors in the computing machine. 
The solution depends on the repeated application of formulas (22) - (30), 
thus eliminating, stepwise, certain groups of unknowns. The system of par- 
titioning as displayed in Fig. 16, is based on the stepwise elimination of 
  
| groups containing twelve unknowns. This arrangement was chosen in order to 
i| minimize the number of zeros in the individual gubmatrices, denoted by B,'s, 
thus increasing the economy of the necessary computations. Denoting the 
s-times reduced system of normal equations in accordance with the well known 
notation used by Gauss, as .S,. 
we obtain: Ao, z [As (8-11 [4 s-1)] 
| Ao, 3 [^s (s-2)]" [4., (8-2) - 8, Bo, 
? 
9 
Bo, 7 A, [4 - Bi Ao, | 
  
i 3i 
where 
| Apt = Ap=B AB, ond fel -BLALA 
| A2 As— Bh (A Y! B, 12:1 - BIAZIY! D 
| As (S-1) = As - 8! [A (5-2) Bs, Jets 5-85. [As ts-2) fs 52 
  
  
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