[blt]

Great explanation and detail. If one faces a badly conditioned problem, one must think about the error inherent to the inputs. Anything measured from real sensors is already corrupted by that perturbation matrix. Even in some perfect scenario like a model generated by CAD, the corresponding physical object is not going to match.

Numerical stability feels like this black art that programmers are scared of, but I maybe it's less scary if you explain the core problem: nothing in the world is a real number, it's always a probability distribution.