[photon-torpedo]

> but practical algorithms with better exponents exist for all of them.

I'm aware of randomized algorithms with better complexity, which come at the cost of only giving approximate results (though the approximation may be perfectly good for practical purposes). See e.g. [1]. Are there other approaches?

[1] https://doi.org/10.1137/090771806

[owlbite]

If the data is Sparse (which is not uncommon for large matrices in the real world), you can exploit the sparsity to do significantly better then O(n**3).