A New Fast Recursive Matrix Multiplication Algorithm - Jelfimova, L. D. (Cybernetics and systems analysis, 2019)
A new recursive algorithm is proposed for multiplying matrices of order n = 2 q ( q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4 μ with μ = 2 q −1 ( q > 0). As compared with the well-known recursive Strassen’s and Winograd–Strassen’s algorithms, the new algorithm minimizes the multiplicative complexity equal to W m ≈ 0.932 n 2.807 multiplication operations at recursive level d = log 2 n −3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated.