Is there any algorithm exist for improving matrix's reciprocal condition?

for example;

1.0e6*

A=[42,1,0;43,0,0;44 1 1]

%A matrix inputs are badly conditioned but I cannot change the form because it is standart form for A matrix. Then I calculate;

N=A'*A  %N looks very bad conditioned due to A

n=A'*L  (L was determined before)

X=N\n

In conclusion, I cannot trust the results.

Answer 1

[Matt J]

Instead of doing

 X=N\n

you should be doing

 X=A\L