[sevensor]

Personally, my biggest reason to prefer LAPACK in general is that its authors have already put a great deal of effort into correctness and numerical stability, so I don't have to. Even basic LAPACK is pretty fast, let alone the optimized libraries. Hand-optimizing my own special case is an absolute last resort.

[pletnes]

Yes, Cramer’s rule (referred to in the article) does not give numerically stable results AFAIK - which is yet another can of worms. Good catch.

[thanatropism]

I don't think I have heard Cramer's rule mentioned without the caveat "but don't use this for real problems".

[pletnes]

It’s useful for certain theoretical proofs in analytic math - or so I’ve heard. Not all math is well suited to be coded into reliable software.