Jelfimova L.D.
Recursive cellular methods of matrix multiplicaion

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(1.14m 2.807) and O(1.17m 2.854) 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. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: cellular analogs of matrix multiplication algorithms, family of cellular matrix multiplication methods, linear algebra, Numerical methods, Cellular analog of matrix multiplication algorithm, Cellular matrix, Cellulars, Family of cellular matrix multiplication method, M-matrices, M-matrix, matrix, MAtrix multiplication, Matrix multiplication algorithm, Multiplicative complexity, Matrix algebra

Cite:
Jelfimova L.D. (2023). Recursive cellular methods of matrix multiplicaion. Cybernetics and Systems Analysis, 59 (3), 10–20. doi: https://doi.org/10.1007/s10559-023-00571-5 http://jnas.nbuv.gov.ua/article/UJRN-0001402505 [In Ukrainian].