New ways to multiply 3 x 3-matrices
New ways to multiply 3 x 3-matrices
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DOI：
10.1016/j.jsc.2020.10.003
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发表时间：
2021-05-01
影响因子：
0.7
通讯作者：
Seidl, Martina
中科院分区：
文献类型：
--
作者：
Heule, Marijn J. H.;Kauers, Manuel;Seidl, Martina
自20世纪70年代以来，已知计算两个3 × 3矩阵的乘积所需的乘法不超过23次。对于非交换系数环，尚不清楚是否也可以通过更少的乘法来完成。然而，有几种相互不等价的方法可以用23次乘法来完成这项工作。在这篇文章中，我们通过提供超过17，000个新的和互不等价的方案来扩展这个列表，这些方案使用23次乘法来乘以3 × 3-矩阵。此外，我们证明了所有这些计划的集合是一个流形的尺寸至少为17。(C)2020爱思唯尔有限公司保留所有权利。
It is known since the 1970s that no more than 23 multiplications are required for computing the product of two 3 x 3-matrices. For non-commutative coefficient rings, it is not known whether it can also be done with fewer multiplications. However, there are several mutually inequivalent ways of doing the job with 23 multiplications. In this article, we extend this list considerably by providing more than 17,000 new and mutually inequivalent schemes for multiplying 3 x 3-matrices using 23 multiplications. Moreover, we show that the set of all these schemes is a manifold of dimension at least 17. (C) 2020 Elsevier Ltd. All rights reserved.