A New Fast Recursive Matrix Multiplication Algorithm

A new recursive algorithm is proposed for multiplying matrices of order n = 2q (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4μ with μ = 2q−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 Wm ≈ 0.932n2.807 multiplication operations at recursive level d = log2n−3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated.