Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
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TLDR
In this article, a new method for accelerating matrix multiplication asymptotically is presented, based on the ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product.About:
This article is published in Journal of Symbolic Computation.The article was published on 1990-03-01 and is currently open access. It has received 2454 citations till now. The article focuses on the topics: Strassen algorithm & Block matrix.read more
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References
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Proceedings ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: A new method for accelerating matrix multiplication asymptotically is presented, by using a basic trilinear form which is not a matrix product, and making novel use of the Salem-Spencer Theorem.
Journal ArticleDOI
On Sets of Integers Which Contain No Three Terms in Arithmetical Progression.
TL;DR: By a modification of Salem and Spencer' method, the better estimate 1-_2/2log2 + e v(N) > N VloggN is shown.
Journal ArticleDOI
Partial and Total Matrix Multiplication
TL;DR: 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.
Journal ArticleDOI
On the Asymptotic Complexity of Matrix Multiplication
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: 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.