research-article

Powers of tensors and fast matrix multiplication

Author:

François Le GallAuthors Info & Claims

ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation

Pages 296 - 303

https://doi.org/10.1145/2608628.2608664

Published: 23 July 2014 Publication History

Abstract

This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic construction also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with existing approaches, this method is based on convex optimization, and thus has polynomial-time complexity. As an application, we use this method to study powers of the construction given by Coppersmith and Winograd [Journal of Symbolic Computation, 1990] and obtain the upper bound ω < 2.3728639 on the exponent of square matrix multiplication, which slightly improves the best known upper bound.

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Cited By

Kansal MSharma VSharma PJäntschi L(2024)A Globally Convergent Iterative Method for Matrix Sign Function and Its Application for Determining the Eigenvalues of a Matrix PencilSymmetry10.3390/sym1604048116:4(481)Online publication date: 16-Apr-2024
https://doi.org/10.3390/sym16040481
Zhao HFan AOuyang XKoutris P(2024)Conjunctive Queries with Negation and Aggregation: A Linear Time CharacterizationProceedings of the ACM on Management of Data10.1145/36511382:2(1-19)Online publication date: 14-May-2024
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Dey DGupta MMohar BShinkar IO'Donnell R(2024)Nearly Optimal Fault Tolerant Distance OracleProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649697(944-955)Online publication date: 10-Jun-2024
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Powers of tensors and fast matrix multiplication

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ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation

July 2014

444 pages

ISBN:9781450325011

DOI:10.1145/2608628

Editor:
Katsusuke Nabeshima
The University of Tokushima, Japan
,
General Chairs:
Kosaku Nagasaka
Kobe University, Japan
,
Franz Winkler
RISC, University Linz, Austria
,
Program Chair:
Agnes Szanto
North Carolina State University

Copyright © 2014 ACM.

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Published: 23 July 2014

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ISSAC '14

ISSAC '14: International Symposium on Symbolic and Algebraic Computation

July 23 - 25, 2014

Kobe, Japan

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ISSAC '14 Paper Acceptance Rate 51 of 96 submissions, 53%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

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https://doi.org/10.3390/sym16040481
Zhao HFan AOuyang XKoutris P(2024)Conjunctive Queries with Negation and Aggregation: A Linear Time CharacterizationProceedings of the ACM on Management of Data10.1145/36511382:2(1-19)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651138
Dey DGupta MMohar BShinkar IO'Donnell R(2024)Nearly Optimal Fault Tolerant Distance OracleProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649697(944-955)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649697
Björklund AKaski PMohar BShinkar IO'Donnell R(2024)The Asymptotic Rank Conjecture and the Set Cover Conjecture Are Not Both TrueProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649656(859-870)Online publication date: 10-Jun-2024
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