The DOI matches its Crossref record; 7 of the 8 references it cites were found in a registry or an index.
Matrix multiplication via arithmetic progressions
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Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“With the use of the Coppersmith-Winograd algorithm, the time complexity of both the KF-based algorithms can be reduced from O ( m 3 ) to O ( m 2 . 375 ) .”
From Real-Time Performance Assessment of High-Order Tremor Estimators Used in a Wearable Tremor Suppression Device (2022) · cites this paper as [41]
In the citing paper
“Therefore, to reduce the time complexity of the KFbased algorithms, a Coppersmith-Winograd algorithm [41] can be used to optimize the matrix operation.”
From Real-Time Performance Assessment of High-Order Tremor Estimators Used in a Wearable Tremor Suppression Device (2022) · cites this paper as [41]
In the citing paper
“It was identified that the use of a Coppersmith-Winograd algorithm can largely reduce the time complexity of the KFbased algorithm to a similar level as the BMFLC.”
From Real-Time Performance Assessment of High-Order Tremor Estimators Used in a Wearable Tremor Suppression Device (2022) · cites this paper as [41]
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 414
Partial and Total Matrix Multiplication
Schönhage, A. (1981) · SIAM Journal on Computing · doi:10.1137/0210032 · Cited by 279
On the Asymptotic Complexity of Matrix Multiplication
Coppersmith, D., & Winograd, S. (1982) · SIAM Journal on Computing · doi:10.1137/0211038 · Cited by 221
Self-citationHow 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
Pan, V. Y. (1978) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1978.34 · Cited by 121
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
Cited by
Sorted by citations
Items 1,001–1,001 of 1,001
Zhou, Y., Habibollahi, Z., Ibrahim, A., Jenkins, M. E., Naish, M. D., & Trejos, A. L. (2022) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2022.3211450 · Cited by 8
Metadata
- Authors
- Coppersmith, D., & Winograd, S.
- Affiliations
- IBM Research - Thomas J. Watson Research Center (US)
- Venue
- Journal of Symbolic Computation
- Publisher
- Elsevier BV
- Published
- 1990-03
- Volume
- 9
- Issue
- 3
- Pages
- 251-280
- ISSN
- 0747-7171 (ISSN-L)
- OpenAlex
- W1979740015
- Cited by
- 2,248
- References
- 8
- Citations by year
- 2026: 18 · 2025: 29 · 2024: 35 · 2023: 39 · 2022: 42 · 2021: 65 · 2020: 77 · 2019: 92 · 2018: 95 · 2017: 72 · 2016: 64 · 2015: 75 · 2014: 94 · 2013: 112 · 2012: 120
- FWCI
- 34.22
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Symbolic Computation (publishedVersion)
- 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, arithmetic progressions, trilinear forms, Strassen's algorithm, matrix exponent
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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