On the Asymptotic Complexity of Matrix Multiplication

On the Asymptotic Complexity of Matrix Multiplication

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 $\omega $, the exponent for matrix multiplication, is a limit point, that is, it cannot be realized by any single al...

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Veröffentlicht in:SIAM journal on computing 1982-08, Vol.11 (3), p.472-492
Hauptverfasser: Coppersmith, D., Winograd, S.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Construction
Multiplication & division
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Zusammenfassung: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 $\omega $, the exponent for matrix multiplication, is a limit point, that is, it cannot be realized by any single algorithm. We also use these results to construct a new algorithm which shows that $\omega < 2.495548$.
ISSN:0097-5397
1095-7111
DOI:10.1137/0211038