The bilinear complexity and practical algorithms for matrix multiplication
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1970-1984
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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 $O(n^{2.7743})$.
@article{ZVMMF_2013_53_12_a2,
author = {A. V. Smirnov},
title = {The bilinear complexity and practical algorithms for matrix multiplication},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1970--1984},
publisher = {mathdoc},
volume = {53},
number = {12},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a2/}
}
TY - JOUR AU - A. V. Smirnov TI - The bilinear complexity and practical algorithms for matrix multiplication JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2013 SP - 1970 EP - 1984 VL - 53 IS - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a2/ LA - ru ID - ZVMMF_2013_53_12_a2 ER -
%0 Journal Article %A A. V. Smirnov %T The bilinear complexity and practical algorithms for matrix multiplication %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2013 %P 1970-1984 %V 53 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a2/ %G ru %F ZVMMF_2013_53_12_a2
A. V. Smirnov. The bilinear complexity and practical algorithms for matrix multiplication. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1970-1984. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a2/