Complexité de la multiplication de matrices (French Wikipedia)

Analysis of information sources in references of the Wikipedia article "Complexité de la multiplication de matrices" in French language version.

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26doi.org

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ams.org

(en) Julian D. Laderman, « A noncommutative algorithm for multiplying 3×3 matrices using 23 multiplications », Bulletin of the American Mathematical Society, vol. 82, n^o 1,‎ 1976, p. 126–128 (DOI 10.1090/S0002-9904-1976-13988-2, lire en ligne).

archive.org

(en) Steven Skiena, The Algorithm Design Manual, Springer, 2008 (ISBN 978-1-84800-069-8, DOI 10.1007/978-1-84800-070-4_4, lire en ligne), « Sorting and Searching », p. 45–46, 401–403.
(en) William H. Press, Brian P. Flannery, Saul A. Teukolsky et William T. Vetterling, Numerical Recipes: The Art of Scientific Computing, 2007, 3^e éd. (ISBN 978-0-521-88068-8), 108.

arxiv.org

(en) Ran Duan, Hongxun Wu et Renfei Zhou, « Faster Matrix Multiplication via Asymmetric Hashing », Arxiv,‎ 2022 (arXiv 2210.10173).
(en) Josh Alman et Virginia Vassilevska Williams, « A Refined Laser Method and Faster Matrix Multiplication », 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2021),‎ 2020, p. 522-539 (arXiv 2010.05846, lire en ligne)
(en) Grey Ballard, Austin R. Benson, Alex Druinsky, Benjamin Lipshitz et Oded Schwartz, « Improving the numerical stability of fast matrix multiplication », SIAM Journal on Matrix Analysis and Applications, vol. 37, n^o 4,‎ 2016, p. 1382–1418 (DOI 10.1137/15M1032168, arXiv 1507.00687, S2CID 2853388).
(en) Jean-François Le Gall, « Algebraic complexity theory and matrix multiplication », Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14,‎ 2014, p. 296-303 (DOI 10.1145/2608628.2627493, Bibcode 2014arXiv1401.7714L, arXiv 1401.7714, S2CID 2597483)
(en) Ambainis, Filmus et Le Gall, « Fast Matrix Multiplication: Limitations of the Coppersmith-Winograd Method », Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing (STOC '15), Portland, Oregon, USA, Association for Computing Machinery,‎ 14 juin 2015, p. 585–593 (ISBN 978-1-4503-3536-2, DOI 10.1145/2746539.2746554, arXiv 1411.5414, S2CID 8332797, lire en ligne).
(en) Henry Cohn et Chris Umans, « A Group-theoretic Approach to Fast Matrix Multiplication », Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 11–14 October 2003, IEEE Computer Society,‎ 2003, p. 438–449 (DOI 10.1109/SFCS.2003.1238217, arXiv math.GR/0307321, S2CID 5890100).
(en) Francois Le Gall et Florent Urrutia, « Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor », Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics,‎ 1^er janvier 2018, p. 1029–1046 (DOI 10.1137/1.9781611975031.67, arXiv 1708.05622, S2CID 33396059, lire en ligne).
(en) Michael B. Cohen, Yin Tat Lee et Zhao Song, « Solving Linear Programs in the Current Matrix Multiplication Time », Journal of the ACM, vol. 68, n^o 1,‎ 5 janvier 2021, p. 3:1–3:39 (DOI 10.1145/3424305, arXiv 1810.07896, S2CID 231955576).
(en) Andreas Rosowski, « Fast Commutative Matrix Algorithm », Arxiv,‎ 27 juillet 2020 (arXiv 1904.07683)

caltech.edu

authors.library.caltech.edu

(en) Henry Cohn, R. Kleinberg, B. Szegedy et Chris Umans, « Group-theoretic Algorithms for Matrix Multiplication », 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05),‎ 2005, p. 379 (DOI 10.1109/SFCS.2005.39, S2CID 41278294, lire en ligne).

digizeitschriften.de

(en) Volker Strassen, « Gaussian elimination is not optimal », Numerische Mathematik, vol. 13, n^o 4,‎ août 1969, p. 354-356 (DOI 10.1007/BF02165411, S2CID 121656251, lire en ligne).

discreteanalysisjournal.com

(en) J. Blasiak, H. Cohn, T. Church, J. Grochow, Naslund, Sawin et Umans, « On cap sets and the group-theoretic approach to matrix multiplication », Discrete Analysis,‎ 2017, p. 1245 (DOI 10.19086/da.1245, S2CID 9687868, lire en ligne).

doi.org

dx.doi.org

(en) Volker Strassen, « Gaussian elimination is not optimal », Numerische Mathematik, vol. 13, n^o 4,‎ août 1969, p. 354-356 (DOI 10.1007/BF02165411, S2CID 121656251, lire en ligne).
(en) Webb Miller, « Computational complexity and numerical stability », SIAM News, vol. 4, n^o 2,‎ 1975, p. 97–107 (DOI 10.1137/0204009, CiteSeer^x 10.1.1.148.9947)
(en) Steven Skiena, The Algorithm Design Manual, Springer, 2008 (ISBN 978-1-84800-069-8, DOI 10.1007/978-1-84800-070-4_4, lire en ligne), « Sorting and Searching », p. 45–46, 401–403.
(en) Grey Ballard, Austin R. Benson, Alex Druinsky, Benjamin Lipshitz et Oded Schwartz, « Improving the numerical stability of fast matrix multiplication », SIAM Journal on Matrix Analysis and Applications, vol. 37, n^o 4,‎ 2016, p. 1382–1418 (DOI 10.1137/15M1032168, arXiv 1507.00687, S2CID 2853388).
(en) Victor Y. Pan, « Strassen's Algorithm is not Optimal: Trilinear Technique of Aggregating, Uniting and Canceling for Constructing Fast Algorithms for Matrix Operations », Proc. 19th FOCS,‎ octobre 1978, p. 166-176 (DOI 10.1109/SFCS.1978.34, S2CID 14348408).
(en) Dario Andrea Bini, Milvio Capovani, Francesco Romani et Grazia Lotti, « $O(n^{2.7799})$ complexity for $n\times n$ approximate matrix multiplication », Information Processing Letters, vol. 8, n^o 5,‎ juin 1979, p. 234-235 (DOI 10.1016/0020-0190(79)90113-3, lire en ligne).
(en) Arnold Schönhage, « Partial and total matrix multiplication », SIAM Journal on Computing, vol. 10, n^o 3,‎ 1981, p. 434-455 (DOI 10.1137/0210032).
(en) Francesco Romani, « Some properties of disjoint sums of tensors related to matrix multiplication », SIAM Journal on Computing, vol. 11, n^o 2,‎ 1982, p. 263-267 (DOI 10.1137/0211020).
(en) Don Coppersmith et Shmuel Winograd, « On the asymptotic complexity of matrix multiplication », Proc. 22nd Annual Symposium on Foundations of Computer Science (FOCS),‎ 1981, p. 82-90 (DOI 10.1109/SFCS.1981.27, S2CID 206558664).
(en) Volker Strassen, « The asymptotic spectrum of tensors and the exponent of matrix multiplication », Proc. 27th Ann. Symp. on Foundation of Computer Science (FOCS),‎ octobre 1986, p. 49-54 (DOI 10.1109/SFCS.1986.52, S2CID 15077423).
(en) Don Coppersmith et Shmuel Winograd, « Matrix multiplication via arithmetic progressions », Journal of Symbolic Computation, vol. 9, n^o 3,‎ mars 1990, p. 251-280 (DOI 10.1016/S0747-7171(08)80013-2 ).
(en) Virginia V. Williams, « Multiplying Matrices Faster than Coppersmith-Winograd », Proc. 44th Symposium on Theory of Computing (STOC), ACM,‎ 2012, p. 887-898 (DOI 10.1145/2213977.2214056, S2CID 14350287).
(en) Jean-François Le Gall, « Algebraic complexity theory and matrix multiplication », Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14,‎ 2014, p. 296-303 (DOI 10.1145/2608628.2627493, Bibcode 2014arXiv1401.7714L, arXiv 1401.7714, S2CID 2597483)
(en) Ambainis, Filmus et Le Gall, « Fast Matrix Multiplication: Limitations of the Coppersmith-Winograd Method », Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing (STOC '15), Portland, Oregon, USA, Association for Computing Machinery,‎ 14 juin 2015, p. 585–593 (ISBN 978-1-4503-3536-2, DOI 10.1145/2746539.2746554, arXiv 1411.5414, S2CID 8332797, lire en ligne).
(en) Henry Cohn, R. Kleinberg, B. Szegedy et Chris Umans, « Group-theoretic Algorithms for Matrix Multiplication », 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05),‎ 2005, p. 379 (DOI 10.1109/SFCS.2005.39, S2CID 41278294, lire en ligne).
(en) Henry Cohn et Chris Umans, « A Group-theoretic Approach to Fast Matrix Multiplication », Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 11–14 October 2003, IEEE Computer Society,‎ 2003, p. 438–449 (DOI 10.1109/SFCS.2003.1238217, arXiv math.GR/0307321, S2CID 5890100).
(en) J. Blasiak, H. Cohn, T. Church, J. Grochow, Naslund, Sawin et Umans, « On cap sets and the group-theoretic approach to matrix multiplication », Discrete Analysis,‎ 2017, p. 1245 (DOI 10.19086/da.1245, S2CID 9687868, lire en ligne).
(en) Ran Raz, « On the complexity of matrix product », Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing,‎ 2002, p. 144–151 (ISBN 1581134959, DOI 10.1145/509907.509932, S2CID 9582328).
(en) Francois Le Gall et Florent Urrutia, « Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor », Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics,‎ 1^er janvier 2018, p. 1029–1046 (DOI 10.1137/1.9781611975031.67, arXiv 1708.05622, S2CID 33396059, lire en ligne).
(en) Michael B. Cohen, Yin Tat Lee et Zhao Song, « Solving Linear Programs in the Current Matrix Multiplication Time », Journal of the ACM, vol. 68, n^o 1,‎ 5 janvier 2021, p. 3:1–3:39 (DOI 10.1145/3424305, arXiv 1810.07896, S2CID 231955576).
(en) D. Coppersmith, « Rapid Multiplication of Rectangular Matrices », SIAM Journal on Computing, vol. 11, n^o 3,‎ 1^er août 1982, p. 467–471 (ISSN 0097-5397, DOI 10.1137/0211037, lire en ligne).
(en) Fawzi, A., Balog, M., Huang, A. et al., « Discovering faster matrix multiplication algorithms with reinforcement learning », Nature, n^o 610,‎ 5 octobre 2022, p. 47–53 (DOI 10.1038/s41586-022-05172-4 , lire en ligne).
(en) Julian D. Laderman, « A noncommutative algorithm for multiplying 3×3 matrices using 23 multiplications », Bulletin of the American Mathematical Society, vol. 82, n^o 1,‎ 1976, p. 126–128 (DOI 10.1090/S0002-9904-1976-13988-2, lire en ligne).
Markus Bläser, « On the complexity of the multiplication of matrices of small formats », Journal of Complexity, vol. 19, n^o 1,‎ février 2003, p. 43–60 (DOI 10.1016/S0885-064X(02)00007-9).
(en) Shmuel Winograd, « On multiplication of 2 × 2 matrices », Linear Algebra and Its Applications, vol. 4, n^o 4,‎ 1^er octobre 1971, p. 381–388 (DOI 10.1016/0024-3795(71)90009-7).

doi.org

(en) Ambainis, Filmus et Le Gall, « Fast Matrix Multiplication: Limitations of the Coppersmith-Winograd Method », Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing (STOC '15), Portland, Oregon, USA, Association for Computing Machinery,‎ 14 juin 2015, p. 585–593 (ISBN 978-1-4503-3536-2, DOI 10.1145/2746539.2746554, arXiv 1411.5414, S2CID 8332797, lire en ligne).

ed.ac.uk

era.ed.ac.uk

(en) Andrew James Stothers, On the complexity of matrix multiplication (thèse Ph.D.), University of Edinburgh, 2010 (lire en ligne).

harvard.edu

ui.adsabs.harvard.edu

(en) Jean-François Le Gall, « Algebraic complexity theory and matrix multiplication », Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14,‎ 2014, p. 296-303 (DOI 10.1145/2608628.2627493, Bibcode 2014arXiv1401.7714L, arXiv 1401.7714, S2CID 2597483)

hpi-web.de

eccc.hpi-web.de

(en) Alon, Shpilka et Umans, « On Sunflowers and Matrix Multiplication », Electronic Colloquium on Computational Complexity,‎ avril 2011 (lire en ligne).

issn.org

portal.issn.org

(en) D. Coppersmith, « Rapid Multiplication of Rectangular Matrices », SIAM Journal on Computing, vol. 11, n^o 3,‎ 1^er août 1982, p. 467–471 (ISSN 0097-5397, DOI 10.1137/0211037, lire en ligne).

nature.com

(en) Fawzi, A., Balog, M., Huang, A. et al., « Discovering faster matrix multiplication algorithms with reinforcement learning », Nature, n^o 610,‎ 5 octobre 2022, p. 47–53 (DOI 10.1038/s41586-022-05172-4 , lire en ligne).

psu.edu

citeseerx.ist.psu.edu

(en) Webb Miller, « Computational complexity and numerical stability », SIAM News, vol. 4, n^o 2,‎ 1975, p. 97–107 (DOI 10.1137/0204009, CiteSeer^x 10.1.1.148.9947)

quantamagazine.org

(en) Hartnett, « Matrix Multiplication Inches Closer to Mythic Goal », Quanta Magazine, 23 mars 2021 (consulté le 1^er avril 2021).

sciencedirect.com

(en) Dario Andrea Bini, Milvio Capovani, Francesco Romani et Grazia Lotti, « $O(n^{2.7799})$ complexity for $n\times n$ approximate matrix multiplication », Information Processing Letters, vol. 8, n^o 5,‎ juin 1979, p. 234-235 (DOI 10.1016/0020-0190(79)90113-3, lire en ligne).

semanticscholar.org

api.semanticscholar.org

(en) Volker Strassen, « Gaussian elimination is not optimal », Numerische Mathematik, vol. 13, n^o 4,‎ août 1969, p. 354-356 (DOI 10.1007/BF02165411, S2CID 121656251, lire en ligne).
(en) Grey Ballard, Austin R. Benson, Alex Druinsky, Benjamin Lipshitz et Oded Schwartz, « Improving the numerical stability of fast matrix multiplication », SIAM Journal on Matrix Analysis and Applications, vol. 37, n^o 4,‎ 2016, p. 1382–1418 (DOI 10.1137/15M1032168, arXiv 1507.00687, S2CID 2853388).
(en) Victor Y. Pan, « Strassen's Algorithm is not Optimal: Trilinear Technique of Aggregating, Uniting and Canceling for Constructing Fast Algorithms for Matrix Operations », Proc. 19th FOCS,‎ octobre 1978, p. 166-176 (DOI 10.1109/SFCS.1978.34, S2CID 14348408).
(en) Don Coppersmith et Shmuel Winograd, « On the asymptotic complexity of matrix multiplication », Proc. 22nd Annual Symposium on Foundations of Computer Science (FOCS),‎ 1981, p. 82-90 (DOI 10.1109/SFCS.1981.27, S2CID 206558664).
(en) Volker Strassen, « The asymptotic spectrum of tensors and the exponent of matrix multiplication », Proc. 27th Ann. Symp. on Foundation of Computer Science (FOCS),‎ octobre 1986, p. 49-54 (DOI 10.1109/SFCS.1986.52, S2CID 15077423).
(en) Virginia V. Williams, « Multiplying Matrices Faster than Coppersmith-Winograd », Proc. 44th Symposium on Theory of Computing (STOC), ACM,‎ 2012, p. 887-898 (DOI 10.1145/2213977.2214056, S2CID 14350287).
(en) Jean-François Le Gall, « Algebraic complexity theory and matrix multiplication », Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14,‎ 2014, p. 296-303 (DOI 10.1145/2608628.2627493, Bibcode 2014arXiv1401.7714L, arXiv 1401.7714, S2CID 2597483)
(en) Ambainis, Filmus et Le Gall, « Fast Matrix Multiplication: Limitations of the Coppersmith-Winograd Method », Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing (STOC '15), Portland, Oregon, USA, Association for Computing Machinery,‎ 14 juin 2015, p. 585–593 (ISBN 978-1-4503-3536-2, DOI 10.1145/2746539.2746554, arXiv 1411.5414, S2CID 8332797, lire en ligne).
(en) Henry Cohn, R. Kleinberg, B. Szegedy et Chris Umans, « Group-theoretic Algorithms for Matrix Multiplication », 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05),‎ 2005, p. 379 (DOI 10.1109/SFCS.2005.39, S2CID 41278294, lire en ligne).
(en) Henry Cohn et Chris Umans, « A Group-theoretic Approach to Fast Matrix Multiplication », Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 11–14 October 2003, IEEE Computer Society,‎ 2003, p. 438–449 (DOI 10.1109/SFCS.2003.1238217, arXiv math.GR/0307321, S2CID 5890100).
(en) J. Blasiak, H. Cohn, T. Church, J. Grochow, Naslund, Sawin et Umans, « On cap sets and the group-theoretic approach to matrix multiplication », Discrete Analysis,‎ 2017, p. 1245 (DOI 10.19086/da.1245, S2CID 9687868, lire en ligne).
(en) Ran Raz, « On the complexity of matrix product », Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing,‎ 2002, p. 144–151 (ISBN 1581134959, DOI 10.1145/509907.509932, S2CID 9582328).
(en) Francois Le Gall et Florent Urrutia, « Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor », Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics,‎ 1^er janvier 2018, p. 1029–1046 (DOI 10.1137/1.9781611975031.67, arXiv 1708.05622, S2CID 33396059, lire en ligne).
(en) Michael B. Cohen, Yin Tat Lee et Zhao Song, « Solving Linear Programs in the Current Matrix Multiplication Time », Journal of the ACM, vol. 68, n^o 1,‎ 5 janvier 2021, p. 3:1–3:39 (DOI 10.1145/3424305, arXiv 1810.07896, S2CID 231955576).

siam.org

epubs.siam.org

(en) Francois Le Gall et Florent Urrutia, « Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor », Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics,‎ 1^er janvier 2018, p. 1029–1046 (DOI 10.1137/1.9781611975031.67, arXiv 1708.05622, S2CID 33396059, lire en ligne).
(en) D. Coppersmith, « Rapid Multiplication of Rectangular Matrices », SIAM Journal on Computing, vol. 11, n^o 3,‎ 1^er août 1982, p. 467–471 (ISSN 0097-5397, DOI 10.1137/0211037, lire en ligne).

siam.org

(en) Josh Alman et Virginia Vassilevska Williams, « A Refined Laser Method and Faster Matrix Multiplication », 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2021),‎ 2020, p. 522-539 (arXiv 2010.05846, lire en ligne)

stanford.edu

cs.stanford.edu

(en) Virginia Vassilevska Williams, Multiplying matrices in $O(n^{2.373})$ time (Technical Report), Stanford University (lire en ligne).

worldcat.org

(en) Robert L. Probert, On the complexity of matrix multiplication, University of Waterloo, 1973 (OCLC 1124200063).

zbmath.org

(en) O. M. Makarov, « A noncommutative algorithm for multiplying 5×5 matrices using 102 multiplications », Inf. Process. Lett., vol. 23, n^o 3,‎ 1986, p. 115-117 (zbMATH 0614.65037).