# On the Number of Multiplications Required for Matrix Multiplication

@article{Brockett1976OnTN,
title={On the Number of Multiplications Required for Matrix Multiplication},
author={Roger W. Brockett and David P. Dobkin},
journal={SIAM J. Comput.},
year={1976},
volume={5},
pages={624-628}
}
In this paper we give a new algorithm for matrix multiplication which for n large uses $n^2 + o(n^2 )$ multiplications to multiply $n \times p$ matrices by $p \times n$ matrices provided $p \leqq \log _2 n$. Multiplication and division by 2 is necessary in this algorithm. This is to be compared with $pn^2$ for the standard algorithm and $\simeq p^{.58} n^2 + o(n^2 )$ for an algorithm of Hopcroft and Kerr [1] which, however, requires no multiplication and division by 2.

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 14 CITATIONS

## RAPID MULTIPLICATION OF RECTANGULAR MATRICES *

D. COPPERSMITHS
• 2014
VIEW 14 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

VIEW 1 EXCERPT
CITES BACKGROUND

• ArXiv
• 2018
VIEW 1 EXCERPT
CITES BACKGROUND

• ArXiv
• 2016
VIEW 1 EXCERPT
CITES BACKGROUND

• ICALP
• 2015
VIEW 1 EXCERPT
CITES METHODS

• ArXiv
• 2015
VIEW 1 EXCERPT
CITES BACKGROUND

VIEW 1 EXCERPT
CITES BACKGROUND

VIEW 1 EXCERPT
CITES BACKGROUND

## The Mailman algorithm: A note on matrix-vector multiplication

• Inf. Process. Lett.
• 2009
VIEW 1 EXCERPT
CITES BACKGROUND

## Fast Rectangular Matrix Multiplication and Applications

• J. Complexity
• 1998