15 
4.19 
P Q • 4- • • 
Z (B X UB). + Z (B X UB) V 
j=l 3 k=l k 
D 
P +- Q • +-. • 
Z (B X UF). + z (B UF), 
j=l D k=l K 
or, more compactly, 
(M+B t ÙB)D = -(Q + B t Û F) 
.... 4.20 
Where M and Q correspond to N and P (in equation 4.13) but for the 
system of p points rather than for all n points. Equation 4.20 is 
equivalent to equation 4.13, hence: 
N = M + B Û B 
.... 4.21 
Q + B U F 
. . . . 4.22 
It is now required to express M ^ as a function of the previously 
evaluated inverse N”^. Equation 4.21 may be written as: 
M = N - B t Û B 
. . . . 4.23 
and 
M _1 = (N - B 1 " Û B)" 1 
. . . . 4.24 
A matrix, L, that is temporarily unknown, is now introduced such that 
M" 1 = N" 1 - L 
. . . . 4.25 
From 4.23 and 4.25 one obtains: 
M M 
-1 
(N - B* Û B) (N” 1 - L) = I 
then :