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Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations.
A.M. Ostrowski, On Two Problems in Absract Algebra Connected with Horner’s Rule. In the Studies Presented to R. von Mises
1954
Earlier work this paper cites.
T.S. Motzkin, Evaluation of Polynomials and Evaluation of Rational Functions. Bull. of Amer. Math. Society
1955
Earlier work this paper cites.
J. Todd, Motivation for Working in Numerical Analysis. Communication on Pure and Applied Math
1955
Earlier work this paper cites.
V.Y. Pan, On Methods of Computing the Values of Polynomials. Uspekhi Matematicheskikh Nauk
1966
Earlier work this paper cites.
S. Winograd, On the Number of Multiplications Required to Compute Certain Functions. Proc. of the National Academy of Sciences
1967
Earlier work this paper cites.
S. Winograd, A New Algorithm for Inner Product. IEEE Transaction on Computers
1968
Earlier work this paper cites.
J.E. Hopcroft, L.R. Kerr, Some Techniques for Proving Certain Simple Programs Optimal. Proceedings of the Tenth Annual Symposium on Switching and Automata Theory
1969
Earlier work this paper cites.
V. Strassen, Gaussian Elimination Is Not Optimal. Numerische Math
1969
Earlier work this paper cites.
A. Waksman, On Winograd’s Algorithm for Inner Products. IEEE Transactions on Computers
1970
Earlier work this paper cites.
S. Winograd, On the Number of Multiplications Necessary to Compute Certain Functions. Communications on Pure and Applied Mathematics
1970
Earlier work this paper cites.
J.E. Hopcroft, L.R. Kerr, On Minimizing the Number of Multiplications Necessary for Matrix Multiplication. SIAM J. on Applied Math
1971
Earlier work this paper cites.
A. Schönhage, V. Strassen, Schnelle Multiplikation großer Zahlen. Computing
1971
Earlier work this paper cites.
S. Winograd, On Multiplication of 2 × 2 2\times 2 Matrices. Linear Algebra and Its Applications
1971
Earlier work this paper cites.
C.M. Fiduccia, On Obtaining Upper Bound on the Complexity of Matrix Multiplication. In Analytical Complexity of Computations
1972
Earlier work this paper cites.
C.M. Fiduccia, Polynomial Evaluation via the Division Algorithm: The Fast Fourier Transform Revisited. Proc. 4th Annual ACM Symposium on Theory of Computing (STOC 1972)
1972
Earlier work this paper cites.
V.Y. Pan, On Schemes for the Evaluation of Products and Inverses of Matrices (in Russian). Uspekhi Matematicheskikh Nauk
1972
Earlier work this paper cites.
R.W. Brockett, D. Dobkin, On Optimal Evaluation of a Set of Bilinear Forms. Proc. of the 5th Annual Symposium on the Theory of Computing (STOC 1973)
1973
Earlier work this paper cites.
J.E. Hopcroft, J. Musinski, Duality Applied to Matrix Multiplication and Other Bilinear Forms. SIAM Journal on Computing
1973
Earlier work this paper cites.
V. Strassen, Vermeidung von Divisionen. J. Reine Angew. Math
1973
Earlier work this paper cites.
A.V. Aho, J.E. Hopcroft, J.D. Ullman, The Design and Analysis of Algorithms
1974
Earlier work this paper cites.
J.R. Bunch, J.E. Hopcroft, Triangular Factorization and Inversion by Fast Matrix Multiplication. Mathematics of Computation
1974
Earlier work this paper cites.
M.J. Fischer, M.S. Paterson, String-Matching and Other Products. SIAM–AMS Proc
1974
Earlier work this paper cites.
P.C. Fischer, Further Schemes for Combining Matrix Algorithms. Proceedings of the 2nd Colloquium on Automata, Languages and Programming
1974
Earlier work this paper cites.
R.L. Probert, On the Complexity of Symmetric Computations. Canadian J. of Information Processing and Operational Res
1974
Earlier work this paper cites.
A. Borodin, I. Munro, The Computational Complexity of Algebraic and Numeric Problems
1975
Earlier work this paper cites.
R.W. Brockett, D. Dobkin, On the Number of Multiplications Required for a Matrix Multiplication. SIAM Journal on Computing
1976
Earlier work this paper cites.
R. L. Probert, On the Additive Complexity of Matrix Multiplication. SIAM J. on Computing
1976
Earlier work this paper cites.
R.W. Brockett, D. Dobkin, On Optimal Evaluation of a Set of Bilinear Forms. Linear Algebra and Its Applications
1978
Earlier work this paper cites.
H.F. de Groot, On Varieties of Optimal Algorithms for the Computation of Bilinear Mappings. Theoretical Computer Science
1978
Earlier work this paper cites.
V.Y. Pan, Strassen’s Algorithm Is Not Optimal. Trilinear Technique of Aggregating for Fast Matrix Multiplication. Proc. the 19th Annual IEEE Symposium on Foundations of Computer Science (FOCS’78)
1978
Earlier work this paper cites.
D. Bini, M. Capovani, G. Lotti, F. Romani, O ( n 2.7799 ) O(n^{2.7799}) Complexity for n × n n\times n Approximate Matrix Multiplication. Information Processing Letters
1979
Earlier work this paper cites.
V.Y. Pan, Fields Extension and Trilinear Aggregating, Uniting and Canceling for the Acceleration of Matrix Multiplication. Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science (FOCS’79)
1979
Earlier work this paper cites.
V.Y. Pan, New Fast Algorithms for Matrix Operations. SlAM J. on Computing
1979
Earlier work this paper cites.
F. Romani, private communication, 1979
1979
Earlier work this paper cites.
D. Bini, Relations Between Exact and Approximate Bilinear Algorithms: Applications. Calcolo
1980
Earlier work this paper cites.
D. Bini, G. Lotti, Stability of Fast Algorithms for Matrix Multiplication. Numerische Math
1980
Earlier work this paper cites.
S. Winograd, Arithmetic Complexity of Computations
1980
Earlier work this paper cites.
D. Coppersmith, S. Winograd, On the Asymptotic Complexity of Matrix Multiplication. SIAM J. on Computing
1981
Cited alongside, same era.
V.Y. Pan, The Bit-Operation Complexity of the Convolution of Vectors and of the DFT. Technical report 80-6, Computer Science Dept., SUNY, Albany, NY, 1980. (Abstract in Bulletin of EATCS, 14
1981
Cited alongside, same era.
V.Y. Pan, New Combinations of Methods for the Acceleration of Matrix Multiplications. Computers and Mathematics (with Applications)
1981
Cited alongside, same era.
A. Schönhage, Partial and Total Matrix Multiplication. SIAM J. on Computing
1981
Cited alongside, same era.
D. Coppersmith, Rapid Multiplication of Rectangular Matrices. SIAM Journal on Computing
1982
Cited alongside, same era.
I. Kaporin, The Aggregation and Cancellation Techniques as a Practical Tool for Faster Matrix Multiplication. Theoretical Computer Science
2004
Later among the works it cites.
R. Yuster, U. Zwick, U. Detecting Short Directed Cycles Using Rectangular Matrix Multiplication and Dynamic Programming. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004)
2004
Later among the works it cites.
H. Cohn, R. Kleinberg, B. Szegedy, C. Umans, Group-theoretic Algorithms for Matrix Multiplication. Proceedings of the 46th Annual Symposium on Foundations of Computer Science (FOCS 2005)
2005
Later among the works it cites.
R. Yuster, U. Zwick, Fast Sparse Matrix Multiplication. ACM Transactions on Algorithms
2005
Later among the works it cites.
H. Kaplan, M. Sharir, E. Verbin, Colored Intersection Searching via Sparse Rectangular Matrix Multiplication. In Proceedings of the 22nd ACM Symposium on Computational Geometry
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V.Y. Pan, Trilinear Aggregating with Implicit Canceling for a New Acceleration of Matrix Multiplication. Computers and Mathematics (with Applications)
1982
Cited alongside, same era.
F. Romani, Some Properties of Disjoint Sum of Tensors Related to MM. SIAM J. on Computing
1982
Cited alongside, same era.
A. Schönhage, Asymptotically Fast Algorithms for the Numerical Multiplication and Division of Polynomials with Complex Coefficients. Proc. EUROCAM, Marseille
1982
Cited alongside, same era.
G. Lotti, F. Romani, On the Asymptotic Complexity of Rectangular Matrix Multiplication. Theoretical Computer Science
1983
Cited alongside, same era.
B.W. Char, K.O. Geddes, G.H. Gonnet, GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation. Proceedings of EUROSAM’84, Lecture Notes in Computer Science
1984
Cited alongside, same era.
V.Y. Pan, How Can We Speed up Matrix Multiplication? SIAM Review,
1984
Cited alongside, same era.
V.Y. Pan, Trilinear Aggregating and the Recent Progress in the Asymptotic Acceleration of Matrix Operations. Theoretical Computer Science
1984
Cited alongside, same era.
2006
Later among the works it cites.
J. Demmel, I. Dumitriu, O. Holtz, Fast Linear Algebra Is Stable. Numerische Mathematik
2007
Later among the works it cites.
J. Demmel, I. Dumitriu, O. Holtz, R. Kleinberg, Fast Linear Algebra Is Stable. Numerische Mathematik
2007
Later among the works it cites.
S. Ke, B. Zeng, W. Han, V. Y. Pan, Fast Rectangular Matrix Multiplication and Some Applications. Science in China, Series A: Mathematics
2008
Later among the works it cites.
R.R. Amossen, R. Pagh, Faster Join-projects and Sparse Matrix Multiplications. In Proceedings of the 12th International Conference on Database Theory
2009
Later among the works it cites.
B. Boyer, J.-G. Dumas, C. Pernet, W. Zhou, Memory Efficient Scheduling of Strassen- Winograd’s Matrix Multiplication Algorithm. Proc. Intern. Symposium on Symbolic and Algebraic Computation (ISSAC 2009)
2009
Later among the works it cites.
P. D’Alberto, A. Nicolau, Adaptive Winograd’s Matrix Multiplication. ACM Transactions on Mathematical Software
2009
Later among the works it cites.
J.-G. Dumas, P. Giorgi, C. Pernet, Dense Linear Algebra over Word-size Prime Fields: the FFLAS and FFPACK Packages. ACM Trans. Math. Software
2009
Later among the works it cites.
M. Fürer, Faster Integer Multiplication. SIAM J. on Computing
2009
Later among the works it cites.
T.G. Kolda, B.W. Bader, Tensor Decompositions and Applications. SIAM Review
2009
Later among the works it cites.
I.V. Oseledets, Approximation of Matrices with Logarithmic Number of Parameters. Dokl. Math
2009
Later among the works it cites.
I.V. Oseledets, Approximation of 2 d × 2 d 2^{d}\times 2^{d} Matrices Using Tensor Decomposition. SIAM J. on Matrix Analysis and Applications
2010
Later among the works it cites.
I.V. Oseledets, E.E. Tyrtyshnikov, TT-cross Approximation for Multidimensional Arrays. Linear Algebra Appls
2010
Later among the works it cites.
P. Sankowski, M. Mucha, Fast Dynamic Transitive Closure with Lookahead. Algorithmica
2010
Later among the works it cites.
A.J. Stothers, On the Complexity of Matrix Multiplication. Ph.D. Thesis, University of Edinburgh, 2010
2010
Later among the works it cites.
C.-E. Drevet, Md. N. Islam, É. Schost, Optimization Techniques for Small Matrix Multiplication. Theoretical Computer Science
2011
Later among the works it cites.
B.N. Khoromskij, O ( d log N ) O(d\log N) Quantics Approximation of N N - d d Tensors in High-dimensional Numerical Modeling. Constructive Approximation
2011
Later among the works it cites.
I.V. Oseledets, E.E. Tyrtyshnikov, Algebraic Wavelet Transform via Quantics Tensor Train Decomposition. SIAM J. Scientific Computing
2011
Later among the works it cites.
F. Le Gall, Faster Algorithms for Rectangular Matrix Multiplication. Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2012)
2012
Later among the works it cites.
V. Vassilevska Williams, Multiplying Matrices Faster than Coppersmith–Winograd. Version available at http://theory.stanford.edu/virgi/matrixmult-f.pdf, retrieved on January 30, 2014. Also see Proc. 44th Annual ACM Symposium on Theory of Computing (STOC 2012)
2012
Later among the works it cites.
N. Alon, A. Shpilka, C. Umans, On Sunflowers and Matrix Multiplication. Computational Complexity
2013
Later among the works it cites.
H. Cohn, C. Umans, Fast Matrix Multiplication Using Coherent Configurations. Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2013)
2013
Later among the works it cites.
A.M. Davie, A.J. Stothers, Improved Bound for Complexity of Matrix Multiplication. Proceedings of the Royal Society of Edinburgh
2013
Later among the works it cites.
J. von zur Gathen, J. Gerhard (2013). Modern Computer Algebra
2013
Later among the works it cites.
G.H. Golub, C.F. Van Loan, Matrix Computations
2013
Later among the works it cites.
L. Grasedyck, D. Kressner, C. Tobler, A Literature Survey of Low-rank Tensor Approximation Techniques. GAMM-Mitteilungen
2013
Later among the works it cites.
A.V. Smirnov, The Bilinear Complexity and Practical Algorithms for Matrix Multiplication. Computational Mathematics and Mathematical Physics
2013
Later among the works it cites.
2014
Closest in time.
G. Ballard, E. Carson, J. Demmel, M. Hoemmen, N. Knight, O. Schwartz, Communication Lower Bounds and Optimal Algorithms for Numerical Linear Algebra. Acta Numerica
2014
Closest in time.
J.M. Landsberg, New Lower Bound for the Rank of Matrix Multiplication. SIAM J. on Computing
2014
Closest in time.
F. Le Gall, Powers of Tensors and Fast Matrix Multiplication. Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC 2014)
2014
Closest in time.