I think it went from naïve gaussian through LU and SVD to approximate iterative forms for the top eigenvectors/values. So a good portion of that was not computing the higher order terms that didn't significantly contribute to the results.

Hazy memory though, as it was 25 years back and I've been out of the FEA side of things for 20+ years now.

I will say though -- I was doing some stuff at the time that was burying SuperSparcs for 24 hours at a time, and would now probably run realtime on a watch or phone. (Again, a big mix of hardware advancement, reduced precision for insignificant terms, and generally optimized algos)

FEAs probably involve sparse matrices, which have a lot more complexity than simple dense matrices. For example compute optimal reordering of a generic sparse matrix is iirc NP-complete.