NEW LOWER BOUNDS FOR THE RANK OF MATRIX MULTIPLICATION

被引：16
|
作者：
Landsberg, J. M. [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
SIAM JOURNAL ON COMPUTING | 2014年 / 43卷 / 01期
基金：
美国国家科学基金会;
关键词：
rank; matrix multiplication;
D O I：
10.1137/120880276
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The rank of the matrix multiplication operator for n x n matrices is one of the most studied quantities in algebraic complexity theory. I prove that the rank is at least 3n(2) - o(n(2)). More precisely, for any integer p <= n - 1 the rank is at least (3 - 1/p+1)n(2) - (1 + 2p(2p/p-1))n. The previous lower bound, due to Blaser, was 5/2n(2) - 3n ( the case p = 1). The new bounds improve Blaser's bound for all n > 84. I also prove lower bounds for rectangular matrices that are significantly better than the previous bound.
引用
收藏
页码：144 / 149
页数：6
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