A Fast Non-Commutative Algorithm for Matrix Multiplication

In the paper a non-commutative algorithm for the multiplication of two square matrices of order n is presented. The algorithm requires n3-(n-1)2 multiplications and n3-n2+ 11 (n-1)2 additions. The recursive application of the algorithm for matrices of order nk leads to \(O(_n ^{k\log _n [n^3 - (n - 1)^2 ]} )\)operations to be executed.It is shown that some well-known algorithms are special cases of our algorithm. Finally, an improvement of the algorithm is given for matrices of order 5.