The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Improved bound for complexity of matrix multiplication
Abstract
We give a new bound ω < 2.37369 for the exponent of complexity of matrix multiplication, giving a small improvement on the previous bound obtained by Coppersmith and Winograd. The proof involves an extension of the method used by these authors. We have attempted to make the exposition self-contained.
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“Remark 1.-Bound (4) does not reduce to the QSL induced by the Fubini-Study metric for pure states, except for qubits (N ¼ 2).”
From Tightening Quantum Speed Limits for Almost All States (2018) · cites this paper as [55]
In the citing paper
“For the case of qutrits, T L is never larger than max½T Θ ; T Φ (see Sec. IV of the Supplemental Material [55]).”
From Tightening Quantum Speed Limits for Almost All States (2018) · cites this paper as [55]
Citations
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Metadata
- Authors
- Davie, A. M., & Stothers, A. J.
- Affiliations
- University of Edinburgh (GB)
- Venue
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Publisher
- Cambridge University Press (CUP)
- Published
- 2013-03-18
- Volume
- 143
- Issue
- 2
- Pages
- 351-369
- ISSN
- 0308-2105 (ISSN-L)
- 1473-7124
- OpenAlex
- W2075577372
- Cited by
- 152
- References
- 17
- Citations by year
- 2026: 7 · 2025: 3 · 2024: 7 · 2023: 7 · 2022: 8 · 2021: 10 · 2020: 18 · 2019: 13 · 2018: 19 · 2017: 19 · 2016: 19 · 2015: 10 · 2014: 9 · 2013: 3
- FWCI
- 14.94
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of Edinburgh Section A Mathematics (publishedVersion)
- Funders
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
- Keywords
- matrix multiplication, asymptotic complexity, computational complexity
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