Computational Mathematics and Mathematical Physics

, Volume 53, Issue 12, pp 1781–1795

The bilinear complexity and practical algorithms for matrix multiplication



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(n2.7743).


bilinear complexity rank of the matrix multiplication problem boundary rank algorithms for exact and approximate matrix multiplication least-squares method objective function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Department of JusticeRussian Federal Center of Forensic ScienceMoscowRussia

Personalised recommendations