On the asymptotic complexity of matrix multiplication

@article{Coppersmith1981OnTA,
  title={On the asymptotic complexity of matrix multiplication},
  author={D. Coppersmith and S. Winograd},
  journal={22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)},
  year={1981},
  pages={82-90}
}
  • D. Coppersmith, S. Winograd
  • Published 1981
  • Mathematics, Computer Science
  • 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)
  • The main results of this paper have the following flavor: given one algorithm for multiplying matrices, there exists another, better, algorithm. A consequence of these results is that ω, the exponent for matrix multiplication, is a limit point, that is, cannot be realized by any single algorithm. We also use these results to construct a new algorithm which shows that ω ≪ 2.495364. 
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    References

    SHOWING 1-10 OF 15 REFERENCES
    On the Asymptotic Complexity of Matrix Multiplication
    • 211
    Duality Applied to the Complexity of Matrix Multiplication and Other Bilinear Forms
    • 81
    • PDF
    Partial and Total Matrix Multiplication
    • 221
    The computational complexity of algebraic and numeric problems
    • 427
    Vermeidung von Divisionen.
    • 347
    Gaussian elimination is not optimal
    • 2,240
    • PDF
    Algebra
    • 5,457
    Pan, New Combinations of Methods for the Accerleration of Matrix Multiplication
    • SUNYA Report
    • 1980