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A New Fast Recursive Matrix Multiplication Algorithm

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Abstract

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.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    L. D. Jelfimova

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  1. L. D. Jelfimova
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Correspondence to L. D. Jelfimova.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2019, pp. 33–38.

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Jelfimova, L.D. A New Fast Recursive Matrix Multiplication Algorithm. Cybern Syst Anal 55, 547–551 (2019). https://doi.org/10.1007/s10559-019-00163-2

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  • DOI: https://doi.org/10.1007/s10559-019-00163-2

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