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A Fast Recursive Algorithm for Multiplying Matrices of Order n = 3q (q > 1)

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Cybernetics and Systems Analysis Aims and scope

Abstract

A new fast recursive algorithm is proposed for multiplying matrices of order n = 3q (q > 1). This algorithm is based on the hybrid algorithm for multiplying matrices of odd order n = 3μ (μ = 2q – 1, q > 1), which is used as a basic algorithm for μ = 3q (q > 0). As compared with the well-known block-recursive Laderman’s algorithm, the new algorithm minimizes by 10.4% the multiplicative complexity equal toWm = 0 896n2.854 multiplication operations at recursion level d = log3 n – 3 and reduces the computation vector by three recursion steps. The multiplicative complexity of the basic and recursive algorithms are 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.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2021, pp. 41–51.

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Jelfimova, L.D. A Fast Recursive Algorithm for Multiplying Matrices of Order n = 3q (q > 1). Cybern Syst Anal 57, 205–213 (2021). https://doi.org/10.1007/s10559-021-00345-x

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  • DOI: https://doi.org/10.1007/s10559-021-00345-x

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