In linear algebra, the Coppersmith–Winograd algorithm, named after Don Coppersmith and Shmuel Winograd, was the asymptotically fastest known matrix multiplication algorithm until 2010. It can multiply two
In 2010, Andrew Stothers gave an improvement to the algorithm,
The Coppersmith–Winograd algorithm is frequently used as a building block in other algorithms to prove theoretical time bounds. However, unlike the Strassen algorithm, it is not used in practice because it only provides an advantage for matrices so large that they cannot be processed by modern hardware.
Henry Cohn, Robert Kleinberg, Balázs Szegedy and Chris Umans have re-derived the Coppersmith–Winograd algorithm using a group-theoretic construction. They also showed that either of two different conjectures would imply that the optimal exponent of matrix multiplication is 2, as has long been suspected. However, they were not able to formulate a specific solution leading to a better running-time than Coppersmith-Winograd at the time.