Homs, Roser; Jelisiejew, Joachim; Michałek, Mateusz; Seynnaeve, Tim (2022). Bounds on complexity of matrix multiplication away from Coppersmith–Winograd tensors. Journal of pure and applied algebra, 226(12), p. 107142. Elsevier 10.1016/j.jpaa.2022.107142
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We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, and monomial algebras. We analyze them using Strassen's laser method and obtain an upper bound 2.431 on ω. We also explain how in certain monomial cases using the laser method directly is less profitable than first degenerating. Our results form possible paths in the search for valuable tensors for the laser method away from Coppersmith-Winograd tensors.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Seynnaeve, Tim |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0022-4049 |
Publisher: |
Elsevier |
Language: |
English |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
14 Mar 2023 14:30 |
Last Modified: |
19 Mar 2023 02:15 |
Publisher DOI: |
10.1016/j.jpaa.2022.107142 |
BORIS DOI: |
10.48350/180017 |
URI: |
https://boris.unibe.ch/id/eprint/180017 |
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