Naive MMP (matrix-matrix product) - O(n^3)

Practically efficient: Strassen MMP (http://en.wikipedia.org/wiki/Strassen_algorithm) - O(n^2.8074)

Theoretically fastest: Modified Coppersmith-Winograd algorithm (On^2.3729).

There is certainly a lot to take into consideration: parallelizability, constants in front, lower-order terms.

http://theory.stanford.edu/~virgi/matrixmult-f.pdf

Naive MMP (matrix-matrix product) - O(n^3)

Practically efficient: Strassen MMP (http://en.wikipedia.org/wiki/Strassen_algorithm) - O(n^2.8074)

Theoretically fastest: Modified Coppersmith-Winograd algorithm (On^2.3729).

There is certainly a lot to take into consideration: parallelizability, constants in front, lower-order terms.

http://theory.stanford.edu/~virgi/matrixmult-f.pdf

Dear Mohammed El-dosuky

What I look that the fastest algorithm for matrix multiplication is O(n^2.376); by Don Coppersmith and Shmuel Winograd;Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation [1990].