Group-theoretic algorithms for matrix multiplication
群论
2012-03-15 v1 组合数学
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.
引用
@article{arxiv.math/0511460,
title = {Group-theoretic algorithms for matrix multiplication},
author = {Henry Cohn and Robert Kleinberg and Balazs Szegedy and Christopher Umans},
journal= {arXiv preprint arXiv:math/0511460},
year = {2012}
}
备注
10 pages