Group-theoretic algorithms for matrix multiplication

被引：74

作者：

Cohn, H ^{[1
]}

Kleinberg, R ^{[1
]}

Szegedy, B ^{[1
]}

Umans, C ^{[1
]}

机构：

[1] Microsoft Res, Redmond, WA 98052 USA

来源：

46TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS | 2005年

关键词：

D O I：

10.1109/SFCS.2005.39

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

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

页码：379 / 388

页数：10

共 9 条

[1]

[Anonymous], 1997, GRUNDLEHREN MATH WIS

[2] A group-theoretic approach to fast matrix multiplication [J].