Group-theoretic algorithms for matrix multiplication

Details Group-theoretic algorithms for matrix multiplication Group-theoretic algorithms for matrix multiplication

2005-11-18

arxiv.org/abs/math/0511460v1

Proceedings of the 46th Annual Symposium on Foundations of Computer Science, 23-25 October 2005, Pittsburgh, PA, IEEE Computer

Mathematics

Group Theory

10 pages

Scientific paper

10.1109/SFCS.2005.39

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.

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