The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Partial and Total Matrix Multiplication
Abstract
In 1979 considerable progress was made in estimating the complexity of matrix multiplication. Here the new techniques and recent results are presented, based upon the notion of approximate rank and the observation that certain patterns of partial matrix multiplication (some of the entries of the matrices may be zero) can efficiently be utilized to perform multiplication of large total matrices. By combining Pan’s trilinear technique with a strong version of our compression theorem for the case of several disjoint matrix multiplications it is shown that multiplication of $N \times N$ matrices (over arbitrary fields) is possible in time $O(N^\beta )$, where $\beta $ is a bit smaller than $3\ln 52/\ln 110 \approx 2.522$.
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Citations
Cites
Gaussian elimination is not optimal
Strassen, V. (1969) · Numerische Mathematik · doi:10.1007/bf02165411 · Cited by 2,509
Cited by
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
Matrix multiplication via arithmetic progressions
Coppersmith, D., & Winograd, S. (1987) · Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87 · doi:10.1145/28395.28396 · Cited by 632
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
Improved bound for complexity of matrix multiplication
Davie, A. M., & Stothers, A. J. (2013) · Proceedings of the Royal Society of Edinburgh: Section A Mathematics · doi:10.1017/s0308210511001648 · Cited by 152
Metadata
- Authors
- Schönhage, A.
- Venue
- SIAM Journal on Computing
- Published
- 1981-08
- Volume
- 10
- Issue
- 3
- Pages
- 434-455
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2023724794
- Cited by
- 259
- References
- 1
- FWCI
- 11.37
- Type
- journal article
- Language
- en
- Open access
- closed
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