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We present a new improvement on the laser method for designing fast matrix multiplication algorithms.
On sets of integers which contain no three terms in arithmetical progression
Raphaël Salem and Donald C. Spencer · 1942
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On sets of integers which contain no three terms in arithmetical progression
Felix A. Behrend · 1946
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Gaussian elimination is not optimal
Volker Strassen · 1969
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Strassen’s algorithm is not optimal: Trililnear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations
Victor 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
Dario Bini, Milvio Capovani, Francesco Romani, and Grazia Lotti · 1979
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Partial and total matrix multiplication
Arnold Schönhage · 1981
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Rapid multiplication of rectangular matrices
Don Coppersmith · 1982
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On the asymptotic complexity of matrix multiplication
Don Coppersmith and Shmuel Winograd · 1982
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Some properties of disjoint sums of tensors related to matrix multiplication
Francesco Romani · 1982
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The asymptotic spectrum of tensors and the exponent of matrix multiplication
Volker Strassen · 1986
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Relative bilinear complexity and matrix multiplication
Volker 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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All pairs shortest paths using bridging sets and rectangular matrix multiplication
Uri Zwick · 2002
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SNOPT: An SQP algorithm for large-scale constrained optimization
Philip E. Gill, Walter Murray, and Michael A. Saunders · 2005
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Faster algorithms for finding lowest common ancestors in directed acyclic graphs
Artur Czumaj, Miroslaw Kowaluk, and Andrzej Lingas · 2007
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All-pairs bottleneck paths in vertex weighted graphs
Asaf Shapira, Raphael Yuster, and Uri Zwick · 2011
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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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Further limitations of the known approaches for matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2018
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Limits on all known (and some unknown) approaches to matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2018
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Improved rectangular matrix multiplication using powers of the Coppersmith-Winograd tensor
François Le Gall and Florent Urrutia · 2018
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Limits on the universal method for matrix multiplication
Josh Alman · 2021
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A refined laser method and faster matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2021
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Barriers for fast matrix multiplication from irreversibility
Matthias Christandl, Péter Vrana, and Jeroen Zuiddam · 2021
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Andris Ambainis, Yuval Filmus, and François Le Gall · 2015
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Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, Eric Naslund, William F. Sawin, and Chris Umans · 2017
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Which groups are amenable to proving exponent two for matrix multiplication?
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, and Chris Umans · 2017
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The MathWorks Inc., Natick, Massachusetts, 2022
MATLAB 9.12 (R2022a) · 2022
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Faster matrix multiplication via asymmetric hashing
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Christian Elsholtz, Zach Hunter, Laura Proske, and Lisa Sauermann · 2024
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New bounds for matrix multiplication: from alpha to omega
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Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
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