The Number of the Beast : Reducing Additions in Fast Matrix Multiplication Algorithms for Dimensions up to 666
While a naive algorithm for multiplying two 2 × 2 matrices requires eight multiplications and four additions, Strassen showed how to compute the same matrix product using seven multiplications and 18 additions. Winograd reduced the number of additions to 15, which was assumed to be optimal. However, by introducing a change of basis, Karstadt and Schwartz showed how to lower the number of additions
