Coppersmith–Winograd algorithm
From Wikipedia, the free encyclopedia
In the mathematical discipline of linear algebra, the Coppersmith–Winograd algorithm is the fastest currently known algorithm for square matrix multiplication. It can multiply two 
matrices in 
time (see Big O notation). This is an improvement over the trivial 
time algorithm and the 
time Strassen algorithm. It might be possible to improve the exponent further; however, the exponent must be at least 2 (because an matrix has n2 values, and all of them have to be read at least once to calculate the exact result).
The Coppersmith–Winograd algorithm is frequently used as building block in other algorithms to prove theoretical time bounds, but it appears to be not particularly practical for implementations.
Henry Cohn, Robert Kleinberg, Balázs Szegedy and Christopher Umans have rederived the Coppersmith–Winograd algorithm using a group-theoretic construction.
[edit] References
- Henry Cohn, Robert Kleinberg, Balazs Szegedy, and Chris Umans. Group-theoretic Algorithms for Matrix Multiplication. arXiv:math.GR/0511460. Proceedings of the 46th Annual Symposium on Foundations of Computer Science, 23-25 October 2005, Pittsburgh, PA, IEEE Computer Society, pp. 379–388.
- Don Coppersmith and Shmuel Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9:251–280, 1990.
