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.

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