Optimization techniques for small matrix multiplication
Charles Éric Drevet, Md. Nazrul Islam, Éric Schost · ACM communications in computer algebra · 2011
We tabulate improved costs for the multiplication of matrices of small size, up to 30. Following previous work by Probert &Fisc her [5], Smith [4], and Mezzarobba [2], we base our approach on previous algorithms for small matrices due to Strassen, Winograd, Pan, Laderman, . . . and show how to exploit these standard algorithms in an improved way. We illustrate the use of our results by generating multiplication code for various rings, such as integers, polynomials, differential operators or linear recurrence operators.