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Bounds on complexity of matrix multiplication away from Coppersmith–Winograd tensors

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2022

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Homs, Roser
Jelisiejew, Joachim
Seynnaeve, Tim

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https://doi.org/10.1016/j.jpaa.2022.107142
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Journal of Pure and Applied Algebra. Elsevier Science. 2022, 226(12), 107142. ISSN 0022-4049. eISSN 1873-1376. Available under: doi: 10.1016/j.jpaa.2022.107142

Zusammenfassung

We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, and monomial algebras. We analyse 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.

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510 Mathematik

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ISO 690HOMS, Roser, Joachim JELISIEJEW, Mateusz MICHALEK, Tim SEYNNAEVE, 2022. Bounds on complexity of matrix multiplication away from Coppersmith–Winograd tensors. In: Journal of Pure and Applied Algebra. Elsevier Science. 2022, 226(12), 107142. ISSN 0022-4049. eISSN 1873-1376. Available under: doi: 10.1016/j.jpaa.2022.107142
BibTex
@article{Homs2022-12Bound-57625,
  year={2022},
  doi={10.1016/j.jpaa.2022.107142},
  title={Bounds on complexity of matrix multiplication away from Coppersmith–Winograd tensors},
  number={12},
  volume={226},
  issn={0022-4049},
  journal={Journal of Pure and Applied Algebra},
  author={Homs, Roser and Jelisiejew, Joachim and Michalek, Mateusz and Seynnaeve, Tim},
  note={Article Number: 107142}
}
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