absolute residuals. 
Claerbout, Muir (1973) applied adjustment by 1-norm Por 
blunder detection in geophysical data and ,Benning'. (1972) 
obtained very good results for point interealation. Barrodale 
(1968) analysed numerical data and pointed out the advantages 
of the 1-norm compared to the 2-norm. Adjustment using 1-norm 
is ‚rather insensitive with. regard | *o outliers. among ‘the 
measurements. It. represents a "robust". statistical estimation 
procedure, confer also Dutter (1980). These robust qualities 
of adjustment by the 1-norm can be demonstrated easily by 
considering the case of direct observations. Let us assume a 
file of observations which contains one outlier: 
(2) 2, 2:2» 1003 
We obtain residuals and adjusted values by using the different 
norms: 
a.) 2-norm: 
6 (arithmetio mean) 
adjusted value: 214 
( 9.6, 19.5, 19.6, 13.6 -.78.1) 
1 
residuals: 1 
b.) 1-norm: 
adjusted value: 2.0 (median value) 
residuals: (0, 0, 0, 0, ~98) 
in case. à.) the outlier distorts the adjusted value 
considerably. In. b.) the fifth observation can be identified 
as an outlier definitely. The adjusted value ‘leads to the 
so-called median value. In a file of values ordered according 
to their size, it.is the value that is most in the "middle" (in 
the above example it is the third value). For an even number 
of measurements two values in the middle (and every value 
between these two values) qualify as the median. Inereasing 
the fifth value arbitrarily does not affect the median at all, 
it remains the same. 
Now the question arises whether these robust qualities 
still hold in a more general adjustment model (adjustment of 
observation equations with more than one parameter) and how to 
solve it. 
Adjustment of observation equations using the  1-norm can 
be. stated as follows: 
Ax = 1 + vy 
n (15) 
X MIU 
is] 
Problem (15) is not solvable in the conventional way : by means 
Of differentiation, the Function to be minimized is not a 
differentiable, function. .By replacing x and v .as differences 
of two non-negative values a formulation is obtained which 
leads to a linear program (conf. Fuchs 1982). This linear 
program has a specific form and can be solved by a simplex