[Solved]: Matrix Multiplication Algorithms for Non-Square Matrices

Problem Detail: 

I'm interested in learning about some of the algorithms available for multiplying non-square matrices, yet despite exhaustive Googling efforts I have been unable to find any discussions of such algorithms except for a couple of extremely general pieces of pseudocode that I found on Wikipedia and MIT OCW.

If anyone could pass on some links to papers that discuss these algorithms in greater detail, I would greatly appreciate it! Thanks!

Asked By : Danny

Answered By : Yuval Filmus

There is an algorithm due to Coppersmith (later improved by him) that can multiply an $N \times N^\alpha$ matrix by an $N^\alpha \times N$ matrix in time $\tilde{O}(N^2)$ for some $\alpha > 0$. The state of the art in this regard is a paper by Le Gall achieving a better $\alpha$, though his algorithm is much more complicated than Coppersmith's. Both algorithms are probably impractical. Ryan Williams (Appendix C) explains how to implement Coppersmith's algorithm, which a priori is non-uniform, in the context of a circuit lower bound; later it was shown that Coppersmith's algorithm can be replaced by other ingredients.

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Question Source : http://cs.stackexchange.com/questions/40633