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We consider the techniques behind the current best algorithms for matrix multiplication.
On sets of integers which contain no three terms in arithmetical progression
Raphaël Salem and Donald C Spencer · 1942
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Gaussian elimination is not optimal
Volker Strassen · 1969
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Strassen’s algorithm is not optimal
V. Y. Pan · 1978
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O ( n 2.7799 ) {O}(n^{2.7799}) complexity for n × n n\times n approximate matrix multiplication
D. Bini, M. Capovani, F. Romani, and G. Lotti · 1979
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New fast algorithms for matrix operations
V. Y. Pan · 1980
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On the asymptotic complexity of matrix multiplication
D. Coppersmith and S. Winograd · 1981
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Partial and total matrix multiplication
A. Schönhage · 1981
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The asymptotic spectrum of tensors and the exponent of matrix multiplication
V. Strassen · 1986
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Relative bilinear complexity and matrix multiplication
V. Strassen · 1987
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Matrix multiplication via arithmetic progressions
Don Coppersmith and Shmuel Winograd · 1990
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Rectangular matrix multiplication revisited
Don Coppersmith · 1997
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A group-theoretic approach to fast matrix multiplication
Henry Cohn and Christopher Umans · 2003
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Group-theoretic algorithms for matrix multiplication
Henry Cohn, Robert Kleinberg, Balazs Szegedy, and Christopher Umans · 2005
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Faster algorithms for rectangular matrix multiplication
François Le Gall · 2012
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Multiplying matrices faster than coppersmith-winograd
Virginia Vassilevska Williams · 2012
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personal communication, 2014
Mateusz Michalek · 2014
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Fast matrix multiplication: limitations of the coppersmith-winograd method
Andris Ambainis, Yuval Filmus, and François Le Gall · 2015
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The growth rate of tri-colored sum-free sets
Robert Kleinberg, William F Sawin, and David E Speyer · 2016
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A distribution on triples with maximum entropy marginal
Sergey Norin · 2016
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Proof of a conjecture of kleinberg-sawin-speyer
Luke Pebody · 2016
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Markus Bläser · 2013
Cited alongside, same era.
Improved bound for complexity of matrix multiplication
A.M. Davie and A. J. Stothers · 2013
Cited alongside, same era.
Powers of tensors and fast matrix multiplication
François Le Gall · 2014
Cited alongside, same era.
On cap sets and the group-theoretic approach to matrix multiplication
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A Grochow, Eric Naslund, William F Sawin, and Chris Umans · 2017
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personal communication, 2017
Henry Cohn · 2017
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On large subsets of 𝔽 q n \mathbb{F}_{q}^{n} with no three-term arithmetic progression
Jordan S Ellenberg and Dion Gijswijt · 2017
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Improved rectangular matrix multiplication using powers of the coppersmith-winograd tensor
François Le Gall and Florent Urrutia · 2017
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