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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k112/k11205h.htm

Last modified: March 6, 2012