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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In the citing paper
“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
Cites
Gaussian elimination is not optimal
Strassen, V. (1969) · Numerische Mathematik · doi:10.1007/bf02165411 · Cited by 2,509
Matrix multiplication via arithmetic progressions
Coppersmith, D., & Winograd, S. (1990) · Journal of Symbolic Computation · doi:10.1016/s0747-7171(08)80013-2 · Cited by 2,248
Bürgisser, P., Clausen, M. V., & Shokrollahi, M. A. (1997) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-662-03338-8 · Cited by 1,103
Gaussian Elimination is not Optimal
Trassen, V. (2005) · Cited by 454
On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
Behrend, F. A. (1946) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.32.12.331 · Cited by 414
Partial and Total Matrix Multiplication
Schönhage, A. (1981) · SIAM Journal on Computing · doi:10.1137/0210032 · Cited by 279
O(n2.7799) complexity for n × n approximate matrix multiplication
Bini, D. A., Capovani, M., Romani, F., & Lotti, G. (1979) · Information Processing Letters · doi:10.1016/0020-0190(79)90113-3 · Cited by 232
On the Asymptotic Complexity of Matrix Multiplication
Coppersmith, D., & Winograd, S. (1982) · SIAM Journal on Computing · doi:10.1137/0211038 · Cited by 221
Relative bilinear complexity and matrix multiplication.
Strassen, V. (1987) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.1987.375-376.406 · Cited by 170
On the complexity of matrix multiplication
Stothers, A. J. (2010) · ERA · Cited by 167
Self-citation
Cited by
Sorted by citations
Powers of tensors and fast matrix multiplication
Gall, F. L. (2014) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/2608628.2608664 · Cited by 938
A Refined Laser Method and Faster Matrix Multiplication
Alman, J., & Williams, V. V. (2021) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611976465.32 · Cited by 363
Popular Conjectures Imply Strong Lower Bounds for Dynamic Problems
Abboud, A., & Williams, V. V. (2014) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2014.53 · Cited by 351
Algebraic complexity theory and matrix multiplication
Gall, F. L. (2014) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/2608628.2627493 · Cited by 235
Subcubic Equivalences Between Path, Matrix, and Triangle Problems
Williams, V. V., & Williams, R. (2018) · Journal of the ACM · doi:10.1145/3186893 · Cited by 201
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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