FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 2, PAGES 107-166

The matrix capacity of a tensor

D. V. Zhdanovich

Abstract

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In 1990, D. Coppersmith and S. Winograd published an estimate of the amount of arithmetic operations necessary for the multiplication of square matrices $n$´ n, which equals $O(n2.3755)$. In this article, we make a systematization of the theoretical instruments that were used by D. Coppersmith and S. Winograd for their estimate. The improved estimate $O(n2.373)$ is one of the results of this systematization.

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Last modified: March 6, 2012