biblio

[1]	Jounaïdi Abdeljaoued and Henri Lombardi. Méthodes Matricielles. Introduction à la Complexité Algébrique. Technical Report 1604.00795, arXiv, April 2016. [ arXiv ]
[2]	Krister Ahlander and Hans Munthe-Kaas. Application of the generalized Fourier transform in numerical linear algebra. BIT Numerical Mathematics, 45(4):819--850, December 2005. [ DOI ]
[3]	Alfred V. Aho, Allan Borodin, Robert L. Constable, Robert W. Floyd, Michael A. Harrison, Richard D. Karp, and Raymond H. Strong, editors. 5th Annual ACM Symposium on the theory of computing, April 30 - May 2 1973. [ http ]
[4]	R. R. Aidagulov and M. V. Shamolin. Fast matrix multiplication by using color algebras. Journal of Mathematical Sciences, 227(4):402--406, December 2017. [ DOI ]
[5]	A. Alder and Volker Strassen. The algorithmic complexity of linear algebras. In Andrei P. Ershov and Donald Erwin Knuth, editors, Proceedings on Algorithms in Modern Mathematics and Computer Science, number 122 in Lecture Notes in Computer Science, pages 343--354, Urgench, Usbek, SSSR, September 16-22 1979. [ DOI ]
[6]	Valery Borisovich Alekseev. On the complexity of some algorithms of matrix multiplication. Journal of Algorithms, 6(1):71 -- 85, March 1985. [ DOI ]
[7]	Valery Borisovich Alekseev and A. A. Nazarov. On bilinear complexity of multiplying 2x2-matrix by 2xm-matrix over finite field. Moscow University Computational Mathematics and Cybernetics, 43(4):149--155, October 2019. [ DOI ]
[8]	Valery Borisovich Alekseev and Alexey Vladimirovich Smirnov. On the exact and approximate bilinear complexities of multiplication of 4x2 and 2x2 matrices. Proceedings of the Steklov Institute of Mathematics, 282(1):123--139, October 2013. [ DOI ]
[9]	Boris Alexeev, Michael Forbes, and Jacob Tsimerman. Tensor rank: some lower and upper bounds. Technical Report 1102.0072, arXiv, February 2011. [ DOI \| arXiv ]
[10]	Josh Alman. Faster walsh-hadamard transform and matrix multiplication over finite fields using lookup tables. Technical Report 2211.04643, arXiv, November 2022. [ DOI ]
[11]	Josh Alman and Virginia Vassilevska Williams. Further limitations of the known approaches for matrix multiplication. Technical Report 1712.07246, arXiv, December 2017. [ arXiv ]
[12]	Josh Alman and Virginia Vassilevska Williams. Limits on All Known (and Some Unknown) Approaches to Matrix Multiplication. Technical Report 1810.08671, arXiv, October 2018. [ arXiv ]
[13]	Josh Alman and Virginia Vassilevska Williams. A refined laser method and faster matrix multiplication. Technical Report 2010.05846, arXiv, October 2020.
[14]	Andris Ambainis, Yuval Filmus, and François Le Gall. Fast matrix multiplication: Limitations of the laser method. Technical Report 1411.5414, arXiv, November 2014. [ DOI \| arXiv ]
[15]	N. Anderson and D. Manley. A matrix extension of Winograd's inner product algorithm. Theoretical Computer Science, 131(2):475--477, September 1994. [ DOI ]
[16]	Elena Angelini, Luca Chiantini, and Andrea Mazzon. Identifiability for a class of symmetric tensors. Technical Report 1811.01865, arXiv, November 2018. [ arXiv ]
[17]	anonymous. Representation of finite groups, 2015.
[18]	Viviana Arrigoni and Annalisa Massini. Fast strassen-based AA^t parallel multiplication. Technical Report 1902.02104, arXiv, February 2019. [ arXiv ]
[19]	M. D. Atkinson and S. Lloyd. Bounds on the ranks of some 3-tensors. Linear algebra and its application, 31:19--31, June 1980. [ DOI ]
[20]	Grey Ballard, Austin R. Benson, Alex Druinsky, Benjamin Lipshitz, and Oded Schwartz. Improving the numerical stability of fast matrix multiplication algorithms. Technical Report 1507.0068, arXiv, July 2015. [ arXiv ]
[21]	Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, and Oded Schwartz. Communication-optimal parallel algorithm for Strassen's matrix multiplication. Technical Report 1202.3173, arXiv, February 2012. [ DOI \| arXiv ]
[22]	Grey Ballard, Christian Ikenmeyer, Joseph M. Landsberg, and Nicholas Ryder. The geometry of rank decompositions of matrix multiplication II: 3×3 matrices. Technical Report 1801.00843, arXiv, January 2018. [ arXiv ]
[23]	Edoardo Ballico, Alessandra Bernardi, Matthias Christandl, and Fulvio Gesmundo. On the partially symmetric rank of tensor products of W-states and other symmetric tensors. Technical report, arXiv, 1803.01623, March 2018. [ arXiv ]
[24]	Razvan Barbulescu, Jérémie Detrey, Nicolas Estibals, and Paul Zimmermann. Finding optimal formulae for bilinear maps. In Ferruh Özbudak and Francisco Rodríguez-Henríquez, editors, International Workshop on the Arithmetic of Finite Fields (WAIFI 2012), volume 7369 of Lecture Notes in Computer Science, pages 168--186, Bochum, Germany, July 16-19 2012. Springer. [ DOI \| http ]
[25]	Kashif Bari. On the structure tensor of sl_n. Technical Report 2105.08171, arXiv, May 2021. [ arXiv ]
[26]	Matías Bender, Jean-Charles Faugère, Ludovic Perret, and Elias Tsigaridas. A nearly optimal algorithm to decompose binary forms. Technical Report 1810.12588, arXiv, October 2018. [ arXiv ]
[27]	Gal Beniamini, Nathan Cheng, Olga Holtz, Elaye Karstadt, and Oded Schwartz. Sparsifying the operators of fast matrix multiplication algorithms. Technical Report 2008.03759, arXiv, August 2020. [ arXiv \| .pdf ]
[28]	Gal Beniamini and Oded Schwartz. Fast matrix multiplication via sparse decomposition. In SPAA '19: Proceedings of the 31st annual ACM symposium on Parallel algorithms and architectures, pages 11--22, Phoenix, Arizona, USA, June 22 - 24 2019. Association for Computing Machinery. [ DOI ]
[29]	Austin R. Benson and Grey Ballard. A framework for practical parallel fast matrix multiplication. Technical Report 1409.2908, arXiv, September 2014. [ DOI \| arXiv ]
[30]	Guillaume O. Berger, P.-A. Absil, Lieven De Lathauwer, Raphaël M. Jungers, and Marc Van Barel. Equivalent polyadic decompositions of matrix multiplication tensors. Technical Report 1902.03950, arXiv, February 2019. [ arXiv ]
[31]	Pavel Berkhin and John Brown. A transform approach to fast matrix multiplication. In Jack Dongarra and Jerzy Wasnieski, editors, First International Workshop Parallel Scientific Computing, volume 879, pages 67--79, Lyngby, Denmark, June 20-23 1994. [ DOI ]
[32]	Alessandra Bernardi, Enrico Carlini, Maria Virginia Catalisano, Alessandro Gimigliano, and Alessandro Oneto. The hitchhiker guide to: secant varieties and tensor decomposition. Mathematics, 6(12):314--400, December 2018. [ DOI \| arXiv ]
[33]	Abhishek Bhrushundi, Prahladh Harsha, Pooya Hatami, Swastik Kopparty, and Mrinal Kumar. On Multilinear Forms: Bias, Correlation, and Tensor Rank. Technical Report 1804.09124, arXiv, April 2018. [ arXiv ]
[34]	Dario Andrea Bini. Relations between exact and approximate bilinear algorithms. Applications. Calcolo, 17(1):87--97, January 1980. [ DOI ]
[35]	Dario Andrea Bini, Milvio Capovani, Francesco Romani, and Grazia Lotti. O(n^2.7799) complexity for n×n approximate matrix multiplication. Information Processing Letters, 8(5):234--235, June 1979. [ DOI ]
[36]	Dario Andrea Bini and Grazia Lotti. Stability of fast algorithms for matrix multiplication. Numerische Mathematik, 36(1):63--72, March 1980. [ DOI ]
[37]	Markus Bläser. A (5)/(2)n²-lower bound for the rank of n×n-matrix multiplication over arbitrary fields. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science, pages 45--50, New York City, New York, USA, October 17-18 1999. IEEE Computer Society. [ DOI ]
[38]	Markus Bläser. On the complexity of the multiplication of matrices of small formats. Journal of Complexity, 19(1):43--60, February 2003. [ DOI ]
[39]	Markus Bläser. Complexity of bilinear problems. Technical report, Saarland university, October 2009.
[40]	Markus Bläser, Matthias Christandl, and Jeroen Zuiddam. The border support rank of two-by-two matrix multiplication is seven. Technical Report 1705.09652, arXiv, May 2017. [ arXiv ]
[41]	Markus Bläser and Vladimir Lysikov. On degeneration of tensors and algebras. Technical Report 1606.04253, arXiv, June 2016. [ arXiv ]
[42]	Markus Bläser and Vladimir Lysikov. Slice Rank of Block Tensors and Irreversibility of Structure Tensors of Algebras. In Javier Esparza and Daniel Král, editors, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020), volume 170 of Leibniz International Proceedings in Informatics (LIPIcs), pages 17:1--17:15, Dagstuhl, Germany, August 2020. Schloss Dagstuhl--Leibniz-Zentrum für Informatik. [ DOI \| http ]
[43]	Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, and Chris Umans. Which groups are amenable to proving exponent two for matrix multiplication? Technical Report 1712.02302, arXiv, December 2017. [ arXiv ]
[44]	Jonah Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, and Chris Umans. Matrix multiplication via matrix groups. Technical report, arXiv, April 2022. [ arXiv \| .pdf ]
[45]	Marco Bodrato. A Strassen-like matrix multiplication suited for squaring and higher power computation. In Watt [275], pages 273--280. [ DOI ]
[46]	Brice Boyer and Jean-Guillaume Dumas. Matrix multiplication over word-size modular rings using approximate formulae. Technical Report 00987812, hal, May 2014.
[47]	Brice Boyer, Clément Pernet, and Wei Zhou. Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm. In May [209]. [ DOI ]
[48]	Gregory V. Brad. Algorithms for fast matrix operations. Technical report, University of Wisconsin, December 2005.
[49]	Richard Pierce Brent. Algorithms for matrix multiplication. Technical Report STAN-CS-70-157, Computer Science Department. Standford university, March 1970. [ .pdf ]
[50]	Richard Pierce Brent. Error analysis of algorithms for matrix multiplication and triangular decomposition using Winograd's identity. Numerische Mathematik, 16(2):145--156, November 1970. [ DOI ]
[51]	Roger Ware Brockett and David Dobkin. On the number of multiplication required for matrix multiplication. SIAM Journal of Scientific Computing, 5(4), December 1976. [ DOI ]
[52]	Roger Ware Brockett and David Dobkin. On the optimal evaluation of a set of bilinear forms. Linear algebra and its application, 19(3):207--235, 1978. [ DOI ]
[53]	Nader Hanna Bshouty. On the additive complexity of 2 ×2 matrix multiplication. Information Processing Letters, 56(6):329--335, December 1995. [ DOI ]
[54]	Werner Büchi and Michael Clausen. On a class of primary algebras of minimal rank. Linear algebra and its application, 69:249--268, August 1985. [ DOI ]
[55]	Jaroslaw Buczyński, Elisa Postinghel, and Filip Rupniewski. On Strassen's rank additivity for small three-way tensors. Technical Report 1902.06582, arXiv, February 2019. [ arXiv ]
[56]	Peter Bürgisser, Michael Clausen, and Mohammad Amin Shokrollahi. Algebraic complexity theory, volume 315 of Grundlehren Mathematischen Wissenchaften. Springer, 1997. [ DOI ]
[57]	Peter Bürgisser and Christian Ikenmeyer. Geometric complexity theory and tensor rank. In Lance Fortnow, editor, Proceedings of the 43rd annual ACM symposium on Theory of computing, pages 509 -- 518, San Jose, CA, USA, June 6-8 2011. [ DOI ]
[58]	Peter Bürgisser and Christian Ikenmeyer. Explicit lower bounds via geometric complexity theory. In Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, pages 141--150, Palo Alto, CA, USA, June 1-4 2013. [ DOI ]
[59]	Peter Bürgisser and Christian Ikenmeyer. Fundamental invariants of orbit closures. Technical Report 1511.02927, arXiv, December 2015. [ arXiv ]
[60]	Vladimir Petrovich Burichenko. On symmetries of the Strassen algorithm. Technical Report 1408.6273, arXiv, August 2014. [ arXiv ]
[61]	Vladimir Petrovich Burichenko. Symmetries of matrix multiplications algorithms I. Technical Report 1508.01110, arXiv, August 2015. [ arXiv ]
[62]	Vladimir Petrovich Burichenko. The isotropy group of the matrix multiplication tensor. Technical Report 2210.16565, arXiv, October 2016. [ arXiv ]
[63]	Vladimir Petrovich Burichenko. Non-existence of a short algorithm for multiplication of 3×3 matrices with group s₄×s₃. Technical Report 2211.03404, arXiv, November 2022. [ arXiv ]
[64]	Vladimir Petrovich Burichenko. Non-existence of a short algorithm for multiplication of 3×3 matrices with group s₄×s₃. Technical Report 2211.03404, arXiv, November 2022. [ arXiv ]
[65]	Vladimir Petrovich Burichenko. On automorphism group of a possible short algorithm for multiplication of 3×3 matrices. Technical Report 2211.06485, arXiv, November 2022. [ arXiv ]
[66]	Enrico Carlini, Nathan Grieve, and Luke Oeding. Four lectures on secant varieties. Technical Report 1309.4145, arXiv, September 2013. [ arXiv ]
[67]	Javier Carrasco Serrano. Finite subgroups of sl(2,c) and sl(3,c). Master's thesis, Mathematics institute, University of Warwick, May 2014.
[68]	Alex Casarotti, Alex Massarenti, and Massimiliano Mella. On Comon's and Strassen's conjectures. Technical Report 1810.09338, arXiv, October 2018. [ arXiv ]
[69]	Murat Cenk and M. Anwar Hasan. On the arithmetic complexity of Strassen-like matrix multiplications. Technical Report 107, IACR Cryptology ePrint Archive, February 2013.
[70]	Murat Cenk and M. Anwar Hasan. On the arithmetic complexity of Strassen-like matrix multiplications. Journal of Symbolic Computation, 80(2):484 -- 501, May-June 2017. [ DOI ]
[71]	Philippe Chatelin. Construction de l'algorithme de Strassen (produit de matrices 2 ×2) par identites matricielles entre traces. Technical report, IMAG, November 1980.
[72]	Philippe Chatelin. Une construction de l'algorithme de Winograd pour le produit de deux matrices 2 ×2. Comptes Rendus de l'Académie des sciences, 290, February 1980.
[73]	Philippe Chatelin. On transformations of algorithms to multiply 2×2 matrices. Technical Report 481, IMAG, November 1984.
[74]	Philippe Chatelin. On Laderman's algorithm to multiply 3 ×3 matrices in 23 multiplications. Technical Report 559, IMAG, October 1985.
[75]	Philippe Chatelin. On transformations of algorithms to multiply 2×2 matrices. Information Processing Letters, 22(1):1 -- 5, January 1986. [ DOI ]
[76]	Philippe Chatelin. Une bibliographie sur la complexite de la multiplication de matrices et des problemes associes (1969-1985). Technical Report 582, IMAG, January 1986.
[77]	Philippe Chatelin. Sur une classification de problème pour des ensembles de formes bilinéaires par des polynômes formels. Technical Report 642, IMAG, January 1987.
[78]	Chatelin, Philippe. Spécifiation et manipulations des programmes : cas d'un ensemble de formes bilinéaires. PhD thesis, Université de Grenoblbe, June 1979.
[79]	Luca Chiantini. Hilbert functions and tensor analysis. Technical Report 1807.00642, arXiv, July 2018. [ arXiv ]
[80]	Luca Chiantini, Jonathan D. Hauenstein, Christian Ikenmeyer, Joseph M. Landsberg, and Giorgio Ottaviani. Polynomials and the exponent of matrix multiplication. Technical Report 1706.05074, arXiv, June 2017. [ arXiv ]
[81]	Luca Chiantini, Christian Ikenmeyer, Joseph M. Landsberg, and Giorgio Ottaviani. The geometry of rank decompositions of matrix multiplication I: 2 ×2 matrices. Technical Report 1610.08364, arXiv, October 2016. [ arXiv ]
[82]	Suryajith Chillara, Nutan Limaye, and Srikanth Srinivasan. Small-depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication, with Applications. Technical Report 1710.05481, arXiv, October 2017. [ arXiv ]
[83]	B. V. Chokaev and G. N. Shumkin. Two bilinear (3x3)-matrix multiplication algorithms of complexity 25. Moscow University Computational Mathematics and Cybernetics, 42(1):23--30, January 2018. [ DOI ]
[84]	Matthias Christandl, François Le Gall, Vladimir Lysikov, and Jeroen Zuiddam. Barriers for rectangular matrix multiplication. Technical Report 2003.03019, arXiv, March 2020. [ arXiv ]
[85]	Matthias Christandl, Asger Kjaerulff Jensen, and Jeroen Zuiddam. Tensor rank is not multiplicative under the tensor product. Technical Report 1705.09379, arXiv, May 2017. [ arXiv ]
[86]	Matthias Christandl, Péter Vrana, and Jeroen Zuiddam. Barriers for fast matrix multiplication from irreversibility. Technical Report 1812.06952, arXiv, December 2018. [ arXiv ]
[87]	Matthias Christandl and Jeroen Zuiddam. Tensor surgery and tensor rank. Technical Report 1606.04085, arXiv, August 2016. [ DOI \| arXiv ]
[88]	Michael Clausen and Ulrich Baum. Fast Fourier transforms for symmetric group: theory and implementation. Mathematics of Computation, 61(204):833--847, October 1993. [ DOI ]
[89]	Jacques Cohen and Martin Roth. On the implementation of strassen's fast multiplication algorithm. Acta Informatica, 6(4):341--355, December 1976. [ DOI \| http ]
[90]	Henry Cohn, Robert Kleinberg, Balazs Szegedy, and Christopher Umans. Group-theoretic algorithms for matrix multiplication. In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS '05, pages 379--388. IEEE Computer Society, 23-25 October 2005. [ DOI \| arXiv ]
[91]	Henry Cohn and Christopher Umans. A group-theoretic approach to fast matrix multiplication. In Proceedings of the 44th annual Symposium on Foundation of Computer Science, pages 438--449. IEEE Computer Society, October 11-14 2003. [ DOI \| arXiv ]
[92]	Henry Cohn and Christopher Umans. Fast matrix multiplication using coherent configurations. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1074--1086, New Orleans, LA, USA, January 6-8 2013. [ DOI \| arXiv ]
[93]	Pierre Comon, Lek-Heng Lim, Yang Qi, and Ke Ye. Topology of tensor ranks. Technical Report 1804.08060, arXiv, April 2018. [ arXiv ]
[94]	Austin Conner. A rank 18 Waring decomposition of sM₃ with 432 symmetries. Technical Report 1711.05796, arXiv, November 2017. [ arXiv ]
[95]	Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg, and Emanuele Ventura. Kronecker powers of tensors and strassen's laser method. Technical Report 1909.04785, arXiv, September 2019. [ arXiv \| http ]
[96]	Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg, and Emanuele Ventura. Tensors with maximal symmetries. Technical report, arXiv, September 2019. [ arXiv ]
[97]	Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg, Emanuele Ventura, and Yao Wang. A geometric study of Strassen's asymptotic rank conjecture and its variants. Technical Report 1811.05511, arXiv, November 2018. [ arXiv ]
[98]	Austin Conner, Alicia Harper, and Joseph M Landsberg. New lower bounds for matrix multiplication and the 3×3 determinant. Technical Report 1911.07981, arXiv, November 2019.
[99]	Austin Conner, Hang Huang, and Joseph M. Landsberg. Bad and good news for strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity. Technical Report 2009.11391, arXiv, September 2020. [ arXiv ]
[100]	Don Coppersmith. Rectangular matrix multiplication revisited. Journal of Complexity, 13(1):42--49, March 1997. [ DOI ]
[101]	Don Coppersmith and Shmuel Winograd. Matrix multiplication via arithmetic progressions. In STOC '87: Proceedings of the nineteenth annual ACM conference on Theory of computing, pages 1--6, New York, NY, USA, May 25-27 1987. ACM. [ DOI ]
[102]	Don Coppersmith and Shmuel Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9(3):251--280, March 1990. [ DOI ]
[103]	Nicolas T. Courtois, Gregory V. Bard, and Daniel Hulme. A new general-purpose method to multiply 3 ×3 matrices using only 23 multiplications. Technical Report 1108.2830, arXiv, August 2011. [ arXiv ]
[104]	Svyatoslav Covanov. Improved method to find optimal formulae for bilinear maps. Technical Report 1705.07728, arXiv, May 2017. [ arXiv ]
[105]	Svyatoslav Covanov. Multiplication algorithms: bilinear complexity and fast asymptotic methods. Phd thesis, Université de Lorraine, June 2018.
[106]	Paolo D'Alberto and Alexandru Nicolau. Adaptive Strassen's matrix multiplication. In Proceedings of the 21st Annual International Conference on Supercomputing, ICS '07, pages 284--292, New York, NY, USA, June 17-21 2007. ACM. [ DOI ]
[107]	José Henrique de Morais Goulart and Pierre Comon. On the minimal ranks of matrix pencils and the existence of a best approximate block-term tensor decomposition. Technical Report 1712.05742, arXiv, December 2017. [ arXiv ]
[108]	James Demmel, Ioana Dumitriu, Olga Holtz, and Robert Kleinberg. Fast matrix multiplication is stable. Numerische Mathematik, 106(2):199--224, February 2007. [ DOI ]
[109]	Harm Derksen and Visu Makam. On non-commutative rank and tensor rank. Technical Report 1606.06701, arXiv, June 2016. [ arXiv ]
[110]	Harm Derksen and Visu Makam. Explicit tensors of border rank at least 2d-2 in K^d K^d K^d in arbitrary characteristic. Technical Report 1709.06131, arXiv, September 2017. [ arXiv ]
[111]	Charles-Éric Drevet, Md. Nazrul Islam, and Éric Schost. Optimization techniques for small matrix multiplication. Theoretical Computer Science, 412(22):2219--2236, May 2011. [ DOI ]
[112]	Ran Duan, Hongxun Wu, and Renfei Zhou. Faster matrix multiplication via asymmetric hashing. Technical Report 2210.10173, arXiv, October 2022. [ DOI ]
[113]	Jean-Guillaume Dumas, Laurent Fousse, and Bruno Salvy. Compressed modular matrix multiplication. In Marc Moreno Maza and Stephen M. Watt, editors, Milestones in Computer Algebra (MICA 2008), May 2008. [ arXiv ]
[114]	Jean-Guillaume Dumas, Pascal Giorgi, and Clément Pernet. Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK packages. ACM Transactions on Mathematical Software, 35(3):19:1--42, October 2008. [ DOI \| http \| .pdf ]
[115]	Jean-Guillaume Dumas and Victor Yakovlevich Pan. Fast matrix multiplication and symbolic computation. Technical Report 1612.05766, arXiv, December 2016. [ arXiv ]
[116]	Jean-Guillaume Dumas, Clément Pernet, and Alexandre Sedoglavic. On fast multiplication of a matrix by its transpose. In Leykin [198], pages 162--169. [ DOI \| http ]
[117]	Pranjal Dutta, Fulvio Gesmundo, Christian Ikenmeyer, Gorav Jindal, and Vladimir Lysikov. Border complexity via elementary symmetric polynomials. 2211.07055, arXiv, November 2022. [ arXiv ]
[118]	Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert, Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Francisco J. R. Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, David Silver, Demis Hassabis, and Pushmeet Kohli. Discovering faster matrix multiplication algorithms with reinforcement learning. Nature, 610(7930):47--53, October 2022. [ DOI \| http ]
[119]	Ephraim Feig and Shmuel Winograd. On the direct sum conjecture. Linear Algebra and its Applications, 63:193 -- 219, December 1984. [ DOI \| http ]
[120]	Charles M. Fiduccia. Fast matrix multiplication. In Michael A. Harrison, Ranan B. Banerji, and Jeffrey D. Ullman, editors, STOC '71 Proceedings of the third annual ACM symposium on Theory of computing, pages 45--49, Shaker Heights, OH, USA, May 3-5 1971. [ DOI ]
[121]	Charles M. Fiduccia. On obtaining upper bounds on the complexity of matrix multiplication. In Raymond E. Miller and James W. Thatcher, editors, Complexity of computer computations, pages 31--40, 187--212. Plenum Press, March 1972. [ DOI ]
[122]	Patrick Carl Fischer. Further Schemes for Combining Matrix Algorithms, pages 428--436. Volume 14 of Loeckx [200], July 29-August 2 1974. [ DOI ]
[123]	Patrick Carl Fischer and Robert Lorne Probert. Efficient procedures for using matrix algorithms. In Loeckx [200], pages 413--427. [ DOI ]
[124]	Joel Friedman. Inner rank and lower bounds for matrix multiplication. Technical Report 1706.04225, arXiv, June 2017. [ arXiv ]
[125]	Vyacheslav Futorny, Joshua A. Grochow, and Vladimir V. Sergeichuk. Wildness for tensors. Technical Report 1810.09219, arXiv, October 2018. [ arXiv ]
[126]	Noël Gastinel. Sur le calcul des produits de matrices. Numerische Mathematik, 17(3):222--229, June 1971. [ DOI ]
[127]	Runshi Geng and Joseph M. Landsberg. On the geometry of geometric rank. Technical Report 2012.04679, arXiv, December 2020. [ arXiv ]
[128]	Fulvio Gesmundo. Geometric aspect of iterated matrix multiplication. Journal of Algebra, 461:42--64, September 2016. [ DOI \| arXiv ]
[129]	Fulvio Gesmundo, Christian Ikenmeyer, and Greta Panova. Geometric complexity theory and matrix powering. Technical Report 1611.00827, arXiv, November 2016. [ arXiv ]
[130]	Fulvio Gesmundo and Joseph M. Landsberg. Explicit polynomial sequences with maximal spaces of partial derivatives and a question of K. Mulmuley. Technical Report 1705.03866, arXiv, May 2017. [ arXiv ]
[131]	Fulvio Gesmundo, Alessandro Oneto, and Emanuele Ventura. Partially symmetric variants of Comon's problem via simultaneous rank. Technical Report 1810.07679, arXiv, October 2018. [ arXiv ]
[132]	Pascal Giorgi. Algorithmes et implantations efficaces en algèbre linéaire exacte. PhD thesis, Universté de Montpellier, October 2019.
[133]	Jon Gonzalez-Sanchez, Laureano Gonzalez-Vega, Alejandro Piñera Nicolas, Irene Polo-Blanco, Jorge Caravantes, and Ignacio F. Rua. Analyzing group based matrix multiplication algorithms. In May [209], pages 159--166. [ DOI ]
[134]	Guy Mathias Gouaya. Algebraic and multilinear-algebraic techniques for fast matrix multiplication. Master's thesis, University of South Africa, 2015. [ http ]
[135]	de M. Goulart, J. H. and Pierre Comon. On the minimal ranks of matrix pencils and the existence of a best approximate block-term tensor decomposition. Technical Report 1712.05742, arXiv, June 2018. [ arXiv ]
[136]	Joshua A. Grochow. Unifying known lower bounds via geometric complexity theory. computational complexity, 24(2):393--475, June 2015. [ DOI \| arXiv ]
[137]	Joshua A. Grochow and Cristopher Moore. Matrix multiplication algorithms from group orbits. Technical Report 1612.01527, arXiv, December 2016. [ arXiv ]
[138]	Joshua A. Grochow and Cristopher Moore. Designing Strassen's algorithm. Technical Report 1708.09398, arXiv, August 2017. [ arXiv ]
[139]	Hans Friedrich Groote, de. On varieties of optimal algorithms for the computation of bilinear mappings I. The isotropy group of a bilinear mapping. Theoretical Computer Science, 7(2):1--24, 1978. [ DOI ]
[140]	Hans Friedrich Groote, de. On varieties of optimal algorithms for the computation of bilinear mappings II. Optimal algorithms for 2×2-matrix multiplication. Theoretical Computer Science, 7(2):127--148, 1978. [ DOI ]
[141]	Hans Friedrich Groote, de. Lectures on the complexity of bilinear problems, volume 245 of Lecture Notes in Computer Science. Springer, 1987. [ DOI ]
[142]	Hans Friedrich Groote, de and Joos Heintz. Comutative algebras of minimal rank. Linear algebra and its application, 55:37--68, December 1983. [ DOI ]
[143]	Sarah Hart, Ivo Hedtke, Matthias Müller-Hannemann, and Sandeep Murthy. A fast search algorithm for (m,m,m) triple product property triples and application for 5×5 matrix multiplication. Technical Report 1305.0448, arXiv, May 2013. [ arXiv ]
[144]	Richard Harter. The optimality of Winograd's formula. Communications of the ACM, 15(5):352, May 1972. [ DOI ]
[145]	Johan Haståd. Tensor rank is NP-complete. Journal of Algorithms, 11(4):644--654, December 1990. [ DOI ]
[146]	Jonathan D. Hauenstein, Christian Ikenmeyer, and Joseph M. Landsberg. Equations for lower bounds on border rank. Technical Report 1305.0779, arXiv, July 2013. [ arXiv ]
[147]	Ivo Hedtke and Sandeep Murthy. Search and test algorithms for triple product property triples. Groups Complexity Cryptology, 4(1):111--133, January 2012. [ DOI \| arXiv ]
[148]	Joos Heintz. On the computational complexity of polynomials and bilinear mappings. a survey. In Huguet and Poli [159], pages 269--300.
[149]	Marijn J.H. Heule, Manuel Kauers, and Martina Seidl. Local search for fast matrix multiplication. Technical Report 1903.11391, arXiv, March 2019. [ arXiv ]
[150]	Marijn J.H. Heule, Manuel Kauers, and Martina Seidl. New ways to multiply 3×3-matrices. Technical Report 1905.10192, arXiv, May 2019. [ arXiv ]
[151]	Nicholas John Higham. Stability of a method for multiplying complex matrices with three real matrix multiplications. SIAM Journal on Matrix Analysis and Applications, 13(3):681--687, July 1992. [ DOI ]
[152]	Nicholas John Higham. Accuracy and stability of numerical algorithms. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996. [ DOI ]
[153]	Roser Homs, Joachim Jelisiejew, Mateusz Michalek, and Tim Seynnaeve. Bounds on complexity of matrix multiplication away from cw tensors. Technical Report 2103.12598, arXiv, March 2021. [ arXiv ]
[154]	John Edward Hopcroft and Leslie Robert Kerr. On minimizing the number of multiplication necessary for matrix multiplication. SIAM Journal on Applied Mathematics, 20(1), January 1971. [ DOI ]
[155]	John Edward Hopcroft and Jean Musinski. Duality applied to the complexity of matrix multiplications and other bilinear forms. In Aho et al. [3], pages 73--87. [ DOI ]
[156]	Shenglong Hu and Ke Ye. Multiplicities of eigenvalues of tensors. Technical Report 1412.2831, arXiv, December 2014. [ arXiv ]
[157]	Jianyu Huang, Leslie Rice, Devin A. Matthews, and Robert A. van de Geijn. Generating Families of Practical Fast Matrix Multiplication Algorithms. Technical Report 1611.01120, arXiv, November 2016. [ arXiv ]
[158]	Xiaohan Huang and Victor Yakovlevich Pan. Fast rectangular matrix multiplication and applications. Journal of Complexity, 14(2):257--299, June 1998. [ DOI ]
[159]	Llorenç Huguet and Alain Poli, editors. Applied algebra, algebraic algorithms and error-correcting codes (5th International Conference), volume 356 of Lecture Notes in Computer Science, Menorca, Spain, June 15-19 1989. Springer.
[160]	Christian Ikenmeyer. Geometric complexity theory, tensor rank and Littlewood-Richardson coefficients. PhD thesis, Universität Paderborn, October 2012.
[161]	Christian Ikenmeyer and Vladimir Lysikov. Strassen's 2x2 matrix multiplication algorithm: A conceptual perspective. Technical Report 1708.08083, arXiv, August 2017. [ arXiv ]
[162]	Joseph Ja'ja'. Optimal evaluation of pairs of bilinear forms. In Richard J. Lipton, editor, STOC'78 Proceedings of the tenth annual ACM symposium on theory of computing, pages 173--183, San Diego, CA, USA, May 1-3 1978. [ DOI ]
[163]	Joseph Ja'ja'. On the complexity of bilinear forms with commutativity. SIAM Journal on Computing, 9(4):713--728, November 1980. [ DOI ]
[164]	Joseph Ja'ja' and Jean Takche. Improved lower bounds for some matrix multiplication problems. Information Processing Letters, 21(3):123 -- 127, September 1985. [ DOI ]
[165]	Claude-Pierre Jeannerod, Théo Mary, Clement Pernet, and Daniel S. Roche. Exploiting Fast Matrix Arithmetic in Block Low-Rank Factorizations. Research Report 02008666, hal, February 2019. [ http ]
[166]	Rodney W. Johnson and Aileen M. McLoughlin. Noncommutative bilinear algorithms for 3×3 matrix multiplication. SIAM Journal on Computing, 15(2):595--603, May 1986. [ DOI ]
[167]	K. Kalorkoti. The trace invariant and matrix inversion. Theoretical Computer Science, 59(3):277 -- 286, August 1988. [ DOI ]
[168]	Michael Kaminski, David G. Kirkpatrick, and Nader Hanna Bshouty. Addition requirements for matrix and transposed matrix products. Journal of Algorithms, 9(3):354 -- 364, September 1988. [ DOI \| http ]
[169]	Igor Kaporin. A practical algorithm for faster matrix multiplication. Numerical Linear Algebra with Applications, 6(8):687--700, December 1999. [ DOI ]
[170]	Igor Kaporin. The aggregation and cancellation techniques as a practical tool for faster matrix multiplication. Theoretical Computer Science, 315(2-3):469 -- 510, May 2004. Algebraic and Numerical Algorithms. [ DOI ]
[171]	Elaye Karstadt and Oded Schwartz. Matrix multiplication, a little faster. In Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '17, pages 101--110, New York, NY, USA, July 24--26 2017. ACM. [ DOI ]
[172]	Manuel Kauers and Jakob Moosbauer. The fbhhrbnrssshk-algorithm for multiplication in Z₂^5×5 is still not the end of the story. Technical Report 2210.04045, arXiv, October 2022. [ arXiv \| .pdf ]
[173]	Manuel Kauers and Jakob Moosbauer. Flip graphs for matrix multiplication. Technical report, arXiv, December 2022. [ arXiv ]
[174]	Donald Erwin Knuth. The Art of Computer Programming. Seminumerical Algorithms, volume 2 of Computer Science and Information Processing. Addison Wesley, Reading, Mass., 3 edition, 1997. [ DOI ]
[175]	Swastik Kopparty, Guy Moshkovitz, and Jeroen Zuiddam. Geometric rank of tensors and subrank of matrix multiplication. Technical Report 2002.09472, arXiv, February 2020. [ arXiv ]
[176]	Tomonori Kouya. Tuning Technique for Multiple Precision Dense Matrix Multiplication using Prediction of Computational Time. Technical Report 1710.01839, arXiv, October 2017. [ arXiv ]
[177]	Siddharth Krishna and Viswambhara Makam. On the tensor rank of 3×3 permanent and determinant. Technical Report 1801.00496, arXiv, January 2018. [ arXiv ]
[178]	Richard Kueng and Joel Tropp. Quantum and classical information processing with tensors. Calthec, April 2019.
[179]	Grzegorz Kwasniewski, Marko Kabić, Maciej Besta, Joost VandeVondele, Raffaele Solcà, and Torsten Hoefler. Red-blue pebbling revisited: near optimal parallel matrix-matrix multiplication. Technical Report 1908.09606, arXiv, August 2019. [ arXiv \| http ]
[180]	Julian David Laderman. A noncommutative algorithm for multiplying 3×3 matrices using 23 multiplications. Bulletin of the American Mathematical Society, 82(1):126--128, January 1976. [ DOI ]
[181]	Julian David Laderman, Victor Yakovlevich Pan, and Xuan-He Sha. On practical algorithms for accelerated matrix multiplication. Linear algebra and its application, 162-164:557--588, February 1992. [ DOI ]
[182]	Joseph M. Landsberg. The border rank of the multiplication of 2×2 matrices is seven. Technical Report math/0407224v3, arXiv, April 2006. [ arXiv ]
[183]	Joseph M. Landsberg. Geometry and the complexity of matrix multiplication. Bulletin of the American Mathematical Society, 45(2):247--284, April 2008. [ DOI \| http ]
[184]	Joseph M. Landsberg. Tensors: geometry and applications, volume 128 of Graduate Studies in Mathematics. American Mathematical Society, 2010. [ DOI ]
[185]	Joseph M. Landsberg. Geometric complexity theory: an introduction for geometers. Technical Report 1305.7387v3, arXiv, December 2013. [ arXiv ]
[186]	Joseph M. Landsberg. New lower bounds for the rank of matrix multiplication. SIAM Journal on Computing, 43(1):144--149, 2014. [ DOI \| arXiv ]
[187]	Joseph M. Landsberg. Geometry and complexity theory, volume 169 of Cambridge Studies in Advanced Mathematics. Cambrigde University Press, December 2016. [ DOI ]
[188]	Joseph M. Landsberg. Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science. Technical Report 2108.06263, arXiv, August 2021. [ arXiv ]
[189]	Joseph M. Landsberg. Secant varieties and the complexity of matrix multiplication. Technical Report 2208.00857, arXiv, August 2022. [ arXiv \| .pdf ]
[190]	Joseph M. Landsberg and Mateusz Michalek. On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry. Technical Report 1601.08229, arXiv, January 2016. [ arXiv ]
[191]	Joseph M. Landsberg and Giorgio Ottaviani. New lower bounds for the border rank of matrix multiplication. Theory of computing, 11:285--298, August 2015. [ DOI \| arXiv ]
[192]	Joseph M. Landsberg and Nicholas Ryder. On the geometry of border rank algorithms for n×2 by 2 ×2 matrix multiplication. Technical Report 1509.08323, arXiv, September 2015. [ arXiv ]
[193]	Joseph M. Landsberg and Zach Teitler. On the ranks and border ranks of symmetric tensors. Foundations of Computational Mathematics, 10(3):339--366, June 2010. [ DOI ]
[194]	François Le Gall. Faster algorithms for rectangular matrix multiplication. Technical Report 1204.1111, arXiv, April 2012. [ arXiv ]
[195]	François Le Gall. Powers of tensors and fast matrix multiplication. Technical Report 1401.7714, arXiv, January 2014. [ arXiv ]
[196]	François Le Gall. Complexity of matrix multiplication and bilinear problems, August 2017.
[197]	François Le Gall and Florent Urrutia. Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor. Technical Report 1708.05622, arXiv, August 2017. [ http ]
[198]	Anton Leykin, editor. ISSAC'20: Proceedings of the 2020 International Symposium on Symbolic and Algebraic Computation, Kalamata, Greece, July 20-22 2020. ACM Press.
[199]	Junjie Li, Sanjay Ranka, and Sartaj Sahni. Strassen's matrix multiplication on gpus. In Proceedings of the 2011 IEEE 17th International Conference on Parallel and Distributed Systems (ICPADS '11), pages 157--164, Tainan, Taiwan, September 7-9 2011. [ DOI ]
[200]	Jacques Loeckx, editor. Automata, Languages and Programming: 2nd Colloquium, volume 14 of Lecture Notes in Computer Science, University of Saarbrücken, Germany, July 29-August 2 1974. Springer.
[201]	Grazia Lotti and Francesco Romani. On the asymptotic complexity of rectangular matrix multiplication. Theoretical Computer Science, 23(2):171 -- 185, April 1983. [ DOI ]
[202]	Dmitry A. Lyakhov, Vladimir P. Gerdt, and Dominik L. Michels. Algorithmic verification of linearizability for ordinary differential equations. Technical Report 1702.03829, arXiv, April 2017. [ arXiv ]
[203]	Oleg Mikhailovich Makarov. Using duality for the synthesis of an optimal algorithm involving matrix multiplication. Information Processing Letters, 13(2):48 -- 49, November 1981. [ DOI ]
[204]	Oleg Mikhailovich Makarov. An algorithm for multiplication of 3×3 matrices. Zhurnal Vychislitel'noĬ Matematiki i MatematicheskoĬ Fiziki, 26(2):293--294, 1986. [ DOI ]
[205]	Oleg Mikhailovich Makarov. A noncommutative algorithm for multiplying 5×5 matrices using 102 multiplications. Information Processing Letters, 23(3):115--117, October 1986. [ DOI ]
[206]	Oleg Mikhailovich Makarov. A non-commutative algorithm for multiplying 5×5 matrices using one hundred multiplications. USSR Computational Mathematics and Mathematical Physics, 27(1):205--207, May 1987. [ DOI ]
[207]	Alex Massarenti and Emanuele Raviolo. The rank of n×n matrix multiplication is at least 3n²-2sqrt(2)n^(3)/(2)-3n. Linear algebra and its application, 438(11):4500--4509, June 2013. [ DOI ]
[208]	Alex Massarenti and Emanuele Raviolo. Corrigendum to "the rank of n ×n matrix multiplication is at least 3n²-2sqrt(2)n^(3)/(2)-3n". Linear algebra and its application, 445(Supplement C):369 -- 371, March 2014. [ DOI ]
[209]	John P. May, editor. ISSAC'09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation, Seoul, Republic of Korea, July 28-31 2009. Association for Computing Machinery.
[210]	Benjamin Merkt, Jens Timmer, and Daniel Kaschek. Higher-order Lie symmetries in identifiability and predictability analysis of dynamical models. Physical Review E, 92(1), July 2015. [ DOI ]
[211]	Marc Mezzarobba. Autour de l'évaluation numérique des fonctions D-finies. Master's thesis, École polytechnique, October 2011. [ .pdf ]
[212]	Webb Miller. Computational complexity and numerical stability. In Robert L. Constable, Robert W. Ritchie, Jack W. Carlyle, and Michael A. Harrison, editors, Proceedings of the sixth annual ACM symposium on Theory of computing, STOC '74, pages 317--322, New York, NY, USA, April 30 - May 2 1974. ACM. [ DOI ]
[213]	Peter Lawrence Montgomery. Five, six, and seven-term Karatsuba-like formulae. IEEE Transactions on Computers, 54(3):362--369, March 2005. [ DOI ]
[214]	Jacques Morgenstern. The linear complexity of computation. Journal of the Association for Computing Machinery, 22(2):184--194, April 1975. [ DOI ]
[215]	Md. Nazrul Islam. Optimization techniques for small matrix multiplication. Master's thesis, University of Western Ontario, London, Ontario, Canada, 2009.
[216]	Jiawang Nie and Ke Ye. Hankel tensor decompositions and ranks. Technical Report 1706.03631, arXiv, June 2017. [ arXiv ]
[217]	Luke Oeding and Giorgio Ottaviani. Eigenvectors of tensors and algorithms for Waring decomposition. Journal of Symbolic Computation, 54:9 -- 35, July 2013. [ DOI \| arXiv \| http ]
[218]	Jinsoo Oh, Jin Kim, and Byung-Ro Moon. On the inequivalence of bilinear algorithms for 3×3 matrix multiplication. Information Processing Letters, 113(17):640--645, August 2013. [ DOI ]
[219]	Marc Olive. Géométrie des espaces de tenseurs --- Une approche effective appliquée à la mécanique des milieux continus. PhD thesis, Université d'Aix-Marseille, March 2015.
[220]	Giorgio Ottaviani. A brief survey on tensor rank and tensor decomposition from a geometric perspective, June 2014.
[221]	Giorgio Ottaviani. Complexity of matrix multiplication and tensor rank, February 2014.
[222]	Victor Yakovlevich Pan. New fast algorithms for matrix operations. SIAM Journal on Computing, 9(2):321--342, May 1980. [ DOI ]
[223]	Victor Yakovlevich Pan. New combinations of methods for the acceleration of matrix multiplications. Computers & Mathematics with Applications, 7(1):73--125, 1981. [ DOI ]
[224]	Victor Yakovlevich Pan. Trilinear aggregating with implicit canceling for a new acceleration of matrix multiplication. Computers & Mathematics with Applications, 8(1):23 --34, 1982. [ DOI ]
[225]	Victor Yakovlevich Pan. How can we speed up matrix multiplication? SIAM Review, 26(3):393--415, July 1984. [ DOI ]
[226]	Victor Yakovlevich Pan. How to multiply matrices faster, volume 179 of Lecture Notes in Computer Science. Springer, 1984. [ DOI ]
[227]	Victor Yakovlevich Pan. The techniques of trilinear aggregating and the recent progress in the asymptotic acceleration of matrix operations. Theoretical Computer Science, 33(1):117--138, 1984. [ DOI \| http ]
[228]	de Polignac, Christian. Méthodes optimales de calcul de produits de matrice. PhD thesis, Faculté des sciences de Grenoble, June 1970.
[229]	Robert Lorne Probert. On the complexity of matrix multiplication. PhD thesis, Faculty of Mathematics, University of Waterloo, September 1973.
[230]	Robert Lorne Probert. On the additive complexity of matrix multiplication. SIAM Journal on Computing, 5(2):187--203, June 1976. [ DOI ]
[231]	Robert Lorne Probert and Patrick Carl Fischer. Decomposition techniques for matrix multiplication problems. Utilitas Mathematica, 18:257--267, 1980.
[232]	Hugues Randriam. Gaps between prime numbers and tensor rank of multiplication in finite fields. Technical Report 1801.01055, arXiv, January 2018. [ arXiv ]
[233]	Hugues Randriambololona. Bilinear complexity of algebras and the Chudnovsky--Chudnovsky interpolation method. Journal of Complexity, 28(4):489--517, August 2012. [ DOI ]
[234]	Ran Raz. On the complexity of matrix product. In John Reif, editor, Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing, STOC '02, pages 144--151, New York, NY, USA, May 19-21 2002. Association for Computing Machinery. [ DOI ]
[235]	Sara Robinson. Toward an optimal algorithm for matrix multiplication. SIAM News, 38(9), November 2005.
[236]	Daniel S. Roche. Error correction in fast matrix multiplication and inverse. Technical Report 1802.02270, arXiv, February 2018. [ arXiv ]
[237]	Andreas Rosowski. Fast commutative matrix algorithm. Technical Report 1904.07683, arXiv, April 2019. [ arXiv ]
[238]	Andreas Rosowski. On fast computation of a circulant matrix-vector product. Technical Report 2103.02605, arXiv, March 2021. [ arXiv ]
[239]	Kathryn Rouse. On the efficiency of algorithms for tensor decomposition and their applications. Master's thesis, Wake forest university, May 2018.
[240]	Bruce E. Sagan. The symmetric group: representations, combinatorial algorithms, and symmetric functions, volume 203 of Graduate Texts in Mathematics. Springer, 2001. [ DOI ]
[241]	Nicola Santoro. Extending the four russians' bound to general matrix multiplication. Information Processing Letters, 10(2):87 -- 88, March 1980. [ DOI ]
[242]	G. Schachtel. A noncommutative algorithm for multiplying 5×5 matrices using 103 multiplications. Information Processing Letters, 7(4):180--182, June 1978. [ DOI ]
[243]	Arnold Schönhage. Partial and total matrix multiplication. SIAM Journal on Computing, 10(3), August 1981. [ DOI ]
[244]	Alexandre Sedoglavic. A non-commutative algorithm for multiplying 5×5 matrices using 99 multiplications. Technical Report 1707.06860, arXiv, July 2017. [ arXiv ]
[245]	Alexandre Sedoglavic. Fast matrix multiplication database, December 2017. [ http ]
[246]	Alexandre Sedoglavic. Laderman matrix multiplication algorithm can be constructed using Strassen algorithm and related tensor's isotropies. Technical Report 1703.08298, arXiv, March 2017. [ arXiv ]
[247]	Alexandre Sedoglavic. A non-commutative algorithm for multiplying 7×7 matrices using 250 multiplications. Technical Report hal-01572046, hal, August 2017. [ http ]
[248]	Alexandre Sedoglavic and Alexey Vladimirovich Smirnov. The tensor rank of 5×5 matrices multiplication is bounded by 98 and its border rank by 89. Technical Report 2101.12568, arXiv, January 2021.
[249]	Anna Seigal. Ranks and Symmetric Ranks of Cubic Surfaces. Technical Report 1801.05377, arXiv, jan 2018. [ arXiv ]
[250]	Tim Seynnaeve. Plethysm and fast matrix multiplication. Technical Report 1710.00528, arXiv, October 2017. [ arXiv ]
[251]	Yaroslav Shitov. How hard is the tensor rank? Technical Report 1611.01559, arXiv, November 2016. [ arXiv ]
[252]	Yaroslav Shitov. A counterexample to Strassen's direct sum conjecture. Technical Report 1712.08660, arXiv, December 2017. [ arXiv ]
[253]	Yaroslav Shitov. A counterexample to Comon's conjecture. Technical Report 1705.08740, arXiv, May 2017. [ arXiv ]
[254]	Thomas Sibut-Pinote. Investigations in Computer-Aided Mathematics: Experimentation, Computation and Certification. PhD thesis, December 2017.
[255]	Thomas Sibut-Pinote and Éric Schost. Fast matrix product algorithms: from theory to practice, November 2015.
[256]	Alexey Vladimirovich Smirnov. The bilinear complexity and practical algorithms for matrix multiplication. Computational Mathematics and Mathematical Physics, 53(2):1781--1795, December 2013. [ DOI ]
[257]	Alexey Vladimirovich Smirnov. The Approximate Bilinear Algorithm of Length 46 for Multiplication of 4 x 4 Matrices. Technical Report 1412.1687, arXiv, November 2014. [ arXiv ]
[258]	Alexey Vladimirovich Smirnov. A bilinear algorithm of length 22 for approximate multiplication of 2×7 and 7 × 2 matrices. Computational Mathematics and Mathematical Physics, 55(4):541--545, April 2015. [ DOI ]
[259]	Alexey Vladimirovich Smirnov. On bilinear algorithms for multiplication of 5×5 matrices. Technical Report 321938742, ResearchGate, January 2017. [ http ]
[260]	Alexey Vladimirovich Smirnov. Several bilinear algorithms for matrix multiplication. Technical Report 313064941, ResearchGate, January 2017. [ DOI ]
[261]	Warren D. Smith. Fast matrix multiplication formulae. Technical report, 2002.
[262]	Luca Sodomaco. The product of the eigenvalues of a symmetric tensor. Technical Report 1802.10173, arXiv, February 2018. [ arXiv ]
[263]	Lorenzo Stefani, De. The i/o complexity of hybrid algorithms for square matrix multiplication. Technical Report arXiv:1904.12804, arXiv, April 2019.
[264]	Andrew James Stothers. On the complexity of Matrix Multiplication. PhD thesis, University of Edinburgh, 2010.
[265]	Volker Strassen. Gaussian elimination is not optimal. Numerische Mathematik, 13(4):354--356, August 1969. [ DOI ]
[266]	Volker Strassen. Rank and optimal computation of generic tensors. Linear algebra and its application, 52-53:645--685, July 1983. [ DOI ]
[267]	Volker Strassen. Relative bilinear complexity and matrix multiplication. Journal für die reine und angewandte Mathematik, 375/376:406--443, 1987. [ DOI ]
[268]	Volker Strassen. The asymptotic spectrum of tensors. Journal für die reine und angewandte Mathematik, 384:102--152, 1988. [ DOI ]
[269]	Ondrej Sykora. A fast non-commutative algorithm for matrix multiplication. In Jozef Gruska, editor, Proceedings of the 6th International Symposium on Mathematical Foundations of Computer Science, volume 53 of Lecture Notes in Computer Science, pages 504--512, Tatranská Lomnica, Czechoslovakia, September 5-9 1977. Springer. [ DOI ]
[270]	Petr Tichavsky. Characterization of decomposition of matrix multiplication tensors. Technical Report 2104.05323, arXiv, April 2021. [ arXiv ]
[271]	Andrei Leonovich Toom. The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady, 3:714--716, 1963.
[272]	A. P. Trefilov. On the approximate bilinear complexity of matrix multiplication. Moscow University Computational Mathematics and Cybernetics, 38(4):177--180, Oct 2014. [ DOI ]
[273]	Abraham Waksman. On Winograd's algorithm for inner products. IEEE Transactions on Computers, C-19(4):360--361, April 1970. [ DOI ]
[274]	Hsin-Po Wang and Iwan Duursma. Parity-checked strassen algorithm. Technical Report 2011.15082, arXiv, November 2020. [ arXiv ]
[275]	Stephen M. Watt, editor. ISSAC'10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Munich, Germany, July 25-28 2010. ACM - SIGSAM, ACM Press.
[276]	Shmuel Winograd. A new algorithm for inner product. IEEE Transactions on Computers, 17(7):693--694, July 1968.
[277]	Shmuel Winograd. On multiplication of 2×2 matrices. Linear algebra and its application, 4(4):381 -- 388, October 1971. [ DOI ]
[278]	Ke Ye and Lek-Heng Lim. Fast structured matrix computations: tensor rank and Cohn--Umans method. Technical Report 1601.00292, arXiv, January 2016. [ arXiv ]
[279]	Raphael Yuster and Uri Zwick. Fast sparse matrix multiplication. ACM Transactions on Algorithms, 1(1):2--13, July 2005. [ DOI ]
[280]	Jinjie Zhang and Lek-Heng Lim. Grothendieck constant is norm of Strassen matrix multiplication tensor. Technical Report 1711.04427, arXiv, November 2017. [ arXiv ]

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