arXiv math/05114602005-11-18math.GRmath.CO

Group-theoretic algorithms for matrix multiplication

Henry Cohn, Robert Kleinberg, Balazs Szegedy, Christopher Umans

备注：: 10 pages
发表信息：: Proceedings of the 46th Annual Symposium on Foundations of Computer Science, 23-25 October 2005, Pittsburgh, PA, IEEE Computer Society, pp. 379-388
DOI：: 10.1109/SFCS.2005.39

英文摘要：

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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