strange linear system

Hi, guys, I encountered a strange problem, say, AX=B, where A is
8000-by-8000 matrix, and the largest singular value is around 0.6, the
least singular value is around 1e-18, and the second least singular
value is around 1e-4.

I tried to use SVD to solve this linear system, zeroing the reciprocal
of the least singular value, however, the result is still not correct.

What's the possible reason? And Is there any method better than SVD in
this case?

.

Relevant Pages

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