Duality applied to the complexity of matrix multiplications and other bilinear forms

Authors:
J. Hopcroft;J. Musinski
Affiliations:
-;-
Venue:
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Year:
1973

Citing 1
Cited 3

Fast matrix multiplication

STOC '71 Proceedings of the third annual ACM symposium on Theory of computing

Combining dimensionality and rate of growth arguments for establishing lower bounds on the number of multiplications

STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Optimization techniques for small matrix multiplication

Theoretical Computer Science
Graph expansion analysis for communication costs of fast rectangular matrix multiplication

MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that the dual of an optimal computation gives an optimal computation for a dual problem. An nxm by mxp matrix product is shown to be the dual of an nxp by pxm or an mxn by nxp matrix product implying that each of the matrix products requires the same number of multiplications to compute. Finally an algorithm for computing a single bilinear form over a noncommutative ring with a minimum number of multiplications is derived by considering a dual problem.