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The bilinear complexity and practical algorithms for matrix multiplication

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Abstract

A method for deriving bilinear algorithms for matrix multiplication is proposed. New estimates for the bilinear complexity of a number of problems of the exact and approximate multiplication of rectangular matrices are obtained. In particular, the estimate for the boundary rank of multiplying 3 × 3 matrices is improved and a practical algorithm for the exact multiplication of square n × n matrices is proposed. The asymptotic arithmetic complexity of this algorithm is O(n 2.7743).

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Authors and Affiliations

  1. Department of Justice, Russian Federal Center of Forensic Science, Khokhlovskii pereul. 13-2, Moscow, 109028, Russia

    A. V. Smirnov

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  1. A. V. Smirnov
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Correspondence to A. V. Smirnov.

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Original Russian Text © A.V. Smirnov, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 12, pp. 1970–1984.

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Smirnov, A.V. The bilinear complexity and practical algorithms for matrix multiplication. Comput. Math. and Math. Phys. 53, 1781–1795 (2013). https://doi.org/10.1134/S0965542513120129

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  • DOI: https://doi.org/10.1134/S0965542513120129

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