The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Group-theoretic Algorithms for Matrix Multiplication
Open accessAbstract
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one would imply that the exponent of matrix multiplication is 2.
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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
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Multiplying matrices faster than coppersmith-winograd
Williams, V. V. (2012) · Proceedings of the forty-fourth annual ACM symposium on Theory of computing · doi:10.1145/2213977.2214056 · Cited by 850
Moore, C., & Mertens, S. (2011) · doi:10.1093/acprof:oso/9780199233212.001.0001 · Cited by 347
New applications of the polynomial method: The cap set conjecture and beyond
Grochow, J. (2018) · Bulletin of the American Mathematical Society · doi:10.1090/bull/1648 · Cited by 16
“In fact, the constructions of [24,26,86,123,135] are all instances of a generalization of this called the simultaneous triple product property—in which one embeds several independent copies of matrix multiplication simultaneously—but the preceding definition is already enough to give us the flavor of the connection wi…”
BackgroundMethod
Metadata
- Authors
- Cohn, H., Kleinberg, R., Szegedy, B., & Umans, C.
- Venue
- 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- Publisher
- IEEE
- Published
- 2005-11-15
- Pages
- 379-388
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2153063335
- Cited by
- 201
- References
- 2
- FWCI
- 7.44
- Type
- conference paper
- Language
- en
- Open access
- green
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- Cohn, H., Kleinberg, R., Szegedy, B., & Umans, C. (2005). Group-theoretic Algorithms for Matrix Multiplication. 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05). https://doi.org/10.1109/sfcs.2005.39
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