On Why and How to Minimize the Arithmetic Complexity of Fast Matrix Multiplication Algorithms
Paul Stankovski Wagner
Naively multiplying two $2 \times 2$ matri-
ces requires eight multiplications and four additions.
Strassen showed how to perform the same computation
using seven multiplications and 18 additions. By chang-
ing basis, Karstadt and Schwartz lowered the number of
additions to 12, which they showed to be optimal within
this generalized Karstadt-Schwartz (KS) framework.
We present improved methods for optimizing the
number of additions in Strassen-type matrix multipli-
cation schemes for larger mat