On degeneration of tensors and Algebras

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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.

Original languageEnglish
Title of host publication41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
EditorsAnca Muscholl, Piotr Faliszewski, Rolf Niedermeier
Place of PublicationSaarbrücken/Wadern
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication date1 Aug 2016
Article number19
ISBN (Electronic)9783959770163
DOIs
Publication statusPublished - 1 Aug 2016
Externally publishedYes
Event41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland
Duration: 22 Aug 201626 Aug 2016

Conference

Conference41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
LandPoland
ByKrakow
Periode22/08/201626/08/2016
SeriesLeibniz International Proceedings in Informatics, LIPIcs
Volume58
ISSN1868-8969

    Research areas

  • Bilinear complexity, Border rank, Commutative algebras, Lower bounds

ID: 232711677