On the Asymptotic Complexity of Matrix Multiplication
Don Coppersmith, Shmuel Winograd · SIAM Journal on Computing · 1982
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 $\omega < 2.495548$.