3 r3 K ul gaS ul ul
17
a) The equations g*® Kp\
b) the normal-equations;
c) the solution of Gp„ from the set of equations]
GpoO 8- (i)
d) the making up of the cofactors-tensor.
The mathematical model to which the observations have to be
submitted, is described by the equations:
mp p* up i2\
a o f
p is running from i, ,,b. The observations are p* with cofactors
gaS (see II).
The description of the mathematical model does not change, if
equations (2) are replaced by another set which is dependant on
the first one.
The matrix up is multiplied by the unit lower triangular matrix
A°p (4°= 1 if p o)
A° up P* A° up
pa p o
The corrections e are determined so that
A" u° pa =A" up
p a 1 P o
or
A" up e" A" hp An up p* Ta
pa p o p a r
and
E g'txg is a minimum.
The solution is, using the multipliers of Lagrange
tfccB A" up K
oap pao
or, after putting
A" W= U"
pa a
e* g°*U°Ka. (3)
The normal-equations become:
„as U" Ul K =T".
0 a 0 p
In these equations the coefficients] p a become zero if the A
are solved as follows:
P«3 u1 ul
For U1 Ul o A\ -3-.
a 3 2 u 1 ul
a 0
If p 3 and equation 2 is already replaced, it is seen that
grt u\ ug gas u* ul
Al=and A\ r—etc.
