which may be written in a form analogous to (23) as: 
um Wu PTE | ; à es 
Xo Ma ‘2 witn Ae. * Ap - Ag A, Aj. 
À 
Jo - Ag, A, 4 
Ao 
The computation of X, is then carried out with formula (26). 
Because the sequence of the steps in the process of partitioning is in 
no way restricted, it is possible to write as in (28) and (26) 
X s AU A, ' with Ar 3 A “Ap Ag Ag (29) 
M = L- Ar Ag de 
and of 1 d 
Xo = A» La - A» Ag; Xi (30) 
The method just described obviously eliminates one of the two groups of 
unknowns as chosen by the process of partitioning and solves for the other 
group. If the method is used to partition & system of normal equations at 
any point along its diagonal, it follows from the symmetry of such a system 
that Al = As , Further, it can be shown that in such a case the 
matrix AS in (28) and correspondingly the matrix AT in (29) are again 
  
symmetrically arranged square matrices. 
Because the matrix AP HAT . in formula (21) is non-singular in 
our problem, we may apply the method of partitioning as Just described for the 
purpose of eliminating the k-values from the original normal equation system, 
The reduced normal equation system is, according to formula (27), 
[87 (aP~'AT)" B]a = B(APT'AN)'L (31) 
22 
pra EEE