On the asymptotic complexity of matrix multiplication

@article{Coppersmith1981OnTA,
  title={On the asymptotic complexity of matrix multiplication},
  author={Don Coppersmith and Shmuel Winograd},
  journal={22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)},
  year={1981},
  pages={82-90}
}
  • D. Coppersmith, S. Winograd
  • Published 28 October 1981
  • Computer Science, Mathematics
  • 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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A consequence of these results is that $\omega $, the exponent for matrix multiplication, is a limit point, that is, it cannot be realized by any single algorithm.
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The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that t...
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By combining Pan’s trilinear technique with a strong version of the compression theorem for the case of several disjoint matrix multiplications it is shown that multiplication of N \times N matrices (over arbitrary fields) is possible in time.
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Thank you for downloading the computational complexity of algebraic and numeric problems elsevier computer science library theory of computation series 1. As you may know, people have search numerous…
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The extent to whieh the use of divisions may speed up the evaluation of polynomials is estimated from above. In particular it is shown that for multiplying general matrices the use of divisions does…
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t. Below we will give an algorithm which computes the coefficients of the product of two square matrices A and B of order n from the coefficients of A and B with tess than 4 . 7 n l°g7 arithmetical…
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THIS is a text–book intended primarily for undergraduates. It is designed to give a broad basis of knowledge comprising such theories and theorems in those parts of algebra which are mentioned in the…
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