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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 12, Pages 1970–1984
DOI: https://doi.org/10.7868/S0044466913120168 (Mi zvmmf9955) 		 
This article is cited in 66 scientific papers (total in 66 papers)

The bilinear complexity and practical algorithms for matrix multiplication

A. V. Smirnov

Department of Justice, Russian Federal Center of Forensic Science, Khokhlovskii pereul. 13-2, Moscow, 109028, Russia
Full-text PDF (263 kB) Citations (66)
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DOI: https://doi.org/10.7868/S0044466913120168
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 $3\times 3$ matrices is improved and a practical algorithm for the exact multiplication of square $n\times n$ matrices is proposed. The asymptotic arithmetic complexity of this algorithm is $O(n^{2.7743})$.
Key words: bilinear complexity, rank of the matrix multiplication problem, boundary rank, algorithms for exact and approximate matrix multiplication, least-squares method, objective function.
Received: 19.03.2013
Revised: 04.06.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 12, Pages 1781–1795
DOI: https://doi.org/10.1134/S0965542513120129
Bibliographic databases:
Document Type: Article
UDC: 519.614
Language: Russian
Citation: A. V. Smirnov, “The bilinear complexity and practical algorithms for matrix multiplication”, Zh. Vychisl. Mat. Mat. Fiz., 53:12 (2013), 1970–1984; Comput. Math. Math. Phys., 53:12 (2013), 1781–1795
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    • This publication is cited in the following 66 articles:
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