rpp (rp s?; see n)-
i8
Generally for equation 6 is, assuming that all preceding equations
are replaced:
„OL0 JJP MJ7
A a 15 (p#a). (4)
71 p gxPtyZJe
The new coefficients become
U° Aa Up w (5)
a p a 1 a
and the normal-equations
g«e ï/e C/p T". (6)
a p
This method is one of the main methods of solution by orthogonal -
ization. In the particular case of ga|3 I (a (3) and g0"9 o
(a'^ (3) the method is described in Jordan-Eggert "Handbuch für
Vermessungskunde Band i" as "Reduced condition-equations
because the ^4° represent the coefficients met in the Gaussian
algorithm.
In this way of calculation, the solution of the equations (i)
degenerates in computing the reciprocal values of Goo, and the
products L"o L+a (p cr) are cancelled.
To facilitate the calculations the condition-equations (2) are
submitted to a linear transformation.
It was MPPa MP
with cofactors ga|3.
The transformation is
P3 g«9 Rx.
The inverse transformation is
The new cofactors become, according to the law of propagation
of the moduli:
gay g3p gYE ga3
as gay grs 11 if a an(f SW gYE 0 if
If P« is replaced by the observation p« then the quasi observation
r* for R" is obtained:
r« r)« gap pv e
or yf gap eand d3 gapl T)a.
7)« G«9Cp. (7)
The new conditions are, putting t/£ ga[iwjp
TTo Ruo with cofactors Ga13.
a o
The solution is finally
7)3= IJo K9 (8)
but also, substituting (7) in (8):
Gr3 eY G^ UoKp
