arXiv:math/0511460math.GR
Group-theoretic algorithms for matrix multiplication
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Abstract
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one would imply that the exponent of matrix multiplication is 2.
Fortunately, there's another approach based on group theory that's able to hit n^2.41 and shows some promise. Here's the paper: https://arxiv.org/abs/math/0511460 Here's a set of lecture notes that are simpler to read and give an easy example of how group theoretic methods work…
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