Proceedings of the 46th Annual Symposium on Foundations of Computer Science
Group-theo- retic algorithms for matrix multiplication
作者:
H. Cohn， R. Kleinberg， B. Szegedy and C. Umans.
关键词:
combinatorial mathematics ； group theory ； matrix multiplication ； algebra ； combinatorial mathematics ； group-theoretic algorithm ； matrix multiplication ； Computer science ； Fourier transforms ； Linear algebra
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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