The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Matrix multiplication via arithmetic progressions
Open accessAbstract
We present a new method for accelerating matrix multiplication asymptotically. This work builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. We make novel use of the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression. Our resulting matrix exponent is 2.376.
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Citations
Cites
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 408
Partial and Total Matrix Multiplication
Schönhage, A. (1981) · SIAM Journal on Computing · doi:10.1137/0210032 · Cited by 259
On the Asymptotic Complexity of Matrix Multiplication
Coppersmith, D., & Winograd, S. (1982) · SIAM Journal on Computing · doi:10.1137/0211038 · Cited by 221
Self-citationRelative 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
How to Multiply Matrices Faster
(1984) · Lecture notes in computer science · doi:10.1007/3-540-13866-8 · Cited by 147
On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
Salem, R., & Spencer, D. C. (1942) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.28.12.561 · Cited by 134
The asymptotic spectrum of tensors and the exponent of matrix multiplication
Strassen, V. (1986) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1986.52 · Cited by 120
On the asymptotic complexity of matrix multiplication
Coppersmith, D., & Winograd, S. (1981) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1981.27 · Cited by 57
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Cited by
Discovering faster matrix multiplication algorithms with reinforcement learning
Fawzi, A., Balog, M., Huang, A., Hubert, T., Romera-Paredes, B., Barekatain, M., Novikov, A., R. Ruiz, F. J., Schrittwieser, J., Swirszcz, G., et al. (2022) · Nature · doi:10.1038/s41586-022-05172-4 · Cited by 478
Metadata
- Authors
- Coppersmith, D., & Winograd, S.
- Venue
- Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
- Publisher
- ACM Press
- Published
- 1987
- Pages
- 1-6
- OpenAlex
- W2080063509
- Cited by
- 632
- References
- 8
- FWCI
- 22.40
- Type
- conference paper
- Language
- en
- Open access
- gold
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- Coppersmith, D., & Winograd, S. (1987). Matrix multiplication via arithmetic progressions. Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87. https://doi.org/10.1145/28395.28396
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
