The author proposes two recursive cellular methods for multiplying matrices of even and odd orders, namely, n = 2q r and n = 3q r (q > 1, r is cell order, n / r = m), which are based on the well-known fast cellular methods for multiplying matrices of orders n = 2μr (μ > 1) and n = 3μr (μ > 1), used as basic ones when μ = 2q (q > 0) and μ = 3q (q > 0). The methods of multiplication of cellular (m × m)-matrices deal with numerical (r × r)-cells, vary their order, and are characterized by the lowest (compared to the well-known cellular methods) multiplicative complexity, which equals, respectively, O(1.14m2.807) and O(1.17m2.854) cellular operations of multiplication. The new methods allow obtaining cellular analogs of the well-known matrix multiplication algorithms with as much as possible minimized multiplicative complexity whose estimation is illustrated by the example of the traditional matrix multiplication algorithm.
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Translated from Kibernetyka ta Systemnyi Analiz, No. 3, May–June, 2023, pp. 10–20.
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Jelfimova, L.D. Recursive Cellular Methods of Matrix Multiplication. Cybern Syst Anal 59, 365–374 (2023). https://doi.org/10.1007/s10559-023-00571-5
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DOI: https://doi.org/10.1007/s10559-023-00571-5