Earlier quoted context omitted.
Low overhead in what sense? matmul is kinda complicated and there are varying, complex state-of-the-art algorithms for it, no? And then if you know things about the matrices in advance you can start optimizing for that, which adds another layer of complexity.
There are, but everyone uses variations of the same O(n^3) algorithm taught in college introduction to linear algebra classes because it is numerically stable and can be made extremely fast through tweaks that give spatial locality and good cache characteristics. Meanwhile the asymptomatically faster algorithms have such large constants in their big O notation that they are not worth using. FFT based matrix multiplic…
Isn't the fastest theoretical algorithm something like O(n^2.37) ?