Paper Info
Title
On degeneration of tensors and algebras.
Abstract
An important building block in all current asymptotically fast algorithms for matrix multiplication are tensors with low border rank, that is, tensors whose border rank is equal or very close to their size. To find new asymptotically fast algorithms for matrix multiplication, it seems to be important to understand those tensors whose border rank is as small as possible, so called tensors of minimal border rank.We investigate the connection between degenerations of associative algebras and degenerations of their structure tensors in the sense of Strassen. It allows us to describe an open subset of n*n*n tensors of minimal border rank in terms of smoothability of commutative algebras. We describe the smoothable algebra associated to the Coppersmith-Winograd tensor and prove a lower bound for the border rank of the tensor used in the easy construction of Coppersmith and Winograd.
Year
DOI
Venue
2016
10.4230/LIPIcs.MFCS.2016.19
MFCS
DocType
Volume
ISSN
Conference
abs/1606.04253
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016), LIPIcs vol.58, pp. 19:1--19:11, 2016
Citations 
PageRank 
References 
1
0.38
1
Authors
2
Name
Order
Citations
PageRank
Markus Bläser132634.03
Vladimir Lysikov212.40