research-article

A Strassen-like matrix multiplication suited for squaring and higher power computation

Author:

Marco BodratoAuthors Info & Claims

ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation

Pages 273 - 280

https://doi.org/10.1145/1837934.1837987

Published: 25 July 2010 Publication History

Abstract

Strassen's method is not the asymptotically fastest known matrix multiplication algorithm, but it is the most widely used for large matrices. Since his manuscript was published, a number of variants have been proposed with different addition complexities. Here we describe a new one. The new variant is at least as good as those already known for simple matrix multiplication, but can save operations either for chain products or for squaring. Moreover it can be proved optimal for these tasks. The largest saving is shown for n^th-power computation, in this scenario the additive complexity can be halved, with respect to original Strassen's.

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https://doi.org/10.1007/978-3-031-76930-6_9
Dumas JGrenet B(2024)In-place accumulation of fast multiplication formulaeProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669671(16-25)Online publication date: 16-Jul-2024
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Schwartz OToledo SVaknin NWiernik G(2024)Alternative Basis Matrix Multiplication is Fast and Stable2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS57955.2024.00013(38-51)Online publication date: 27-May-2024
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A Strassen-like matrix multiplication suited for squaring and higher power computation

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cover image ACM Other conferences

ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation

July 2010

366 pages

ISBN:9781450301503

DOI:10.1145/1837934

Program Chair:
Wolfram Koepf
London, Ontario, Canada

Copyright © 2010 ACM.

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Published: 25 July 2010

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ISSAC '10: International Symposium on Symbolic and Algebraic Computation

July 25 - 28, 2010

Munich, Germany

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ISSAC '10 Paper Acceptance Rate 45 of 110 submissions, 41%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Respondek JRespondek J(2025)Applications of the Fast Matrix Multiplication AlgorithmsFast Matrix Multiplication with Applications10.1007/978-3-031-76930-6_9(177-228)Online publication date: 27-Feb-2025
https://doi.org/10.1007/978-3-031-76930-6_9
Dumas JGrenet B(2024)In-place accumulation of fast multiplication formulaeProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669671(16-25)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669671
Schwartz OToledo SVaknin NWiernik G(2024)Alternative Basis Matrix Multiplication is Fast and Stable2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS57955.2024.00013(38-51)Online publication date: 27-May-2024
https://doi.org/10.1109/IPDPS57955.2024.00013
Hadas TSchwartz O(2023)Towards Practical Fast Matrix Multiplication based on Trilinear AggregationProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597099(289-297)Online publication date: 24-Jul-2023
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Morain FMaza MZhi L(2022)Implementing the Thull-Yap Algorithm for Computing Euclidean Remainder SequencesProceedings of the 2022 International Symposium on Symbolic and Algebraic Computation10.1145/3476446.3536188(197-205)Online publication date: 4-Jul-2022
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Dumas JPernet CSedoglavic AEmiris IZhi LMantzaflaris A(2020)On fast multiplication of a matrix by its transposeProceedings of the 45th International Symposium on Symbolic and Algebraic Computation10.1145/3373207.3404021(162-169)Online publication date: 20-Jul-2020
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Karstadt ESchwartz O(2020)Matrix Multiplication, a Little FasterJournal of the ACM10.1145/336450467:1(1-31)Online publication date: 15-Jan-2020
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Karppa MKaski PChan T(2019)Probabilistic tensors and opportunistic boolean matrix multiplicationProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310466(496-515)Online publication date: 6-Jan-2019
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Pan V(2018)Fast matrix multiplication and its algebraic neighbourhoodSbornik: Mathematics10.1070/SM8833208:11(1661-1704)Online publication date: 29-Jan-2018
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