Strassen's algorithm is not optimally accurate

Dumas, Jean-Guillaume; Pernet, Clément; Sedoglavic, Alexandre

Document type :

Communication dans un congrès avec actes

DOI :

10.1145/3666000.3669697

Title :

Strassen's algorithm is not optimally accurate

Author(s) :

Dumas, Jean-Guillaume [Auteur]
Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie [CASC]
Pernet, Clément [Auteur]
Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie [CASC]
Sedoglavic, Alexandre [Auteur]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Université de Lille

Scientific editor(s) :

Shaoshi Chen

Conference title :

49th International Symposium on Symbolic and Algebraic Computation (ISSAC'24)

Conference organizers(s) :

ACM SIGSAM

City :

Raleigh, NC

Country :

Etats-Unis d'Amérique

Start date of the conference :

2024-07-15

Publisher :

ACM

Publication place :

Raleigh, NC, USA

Publication date :

2024-07-16

HAL domain(s) :

Informatique [cs]/Analyse numérique [cs.NA]
Informatique [cs]/Calcul formel [cs.SC]

English abstract : [en]

We propose a non-commutative algorithm for multiplying 2×2 matrices using 7 coefficient products. This algorithm reaches simultaneously a better accuracy in practice compared to previously known such fast algorithms, and ...
Show more >We propose a non-commutative algorithm for multiplying 2×2 matrices using 7 coefficient products. This algorithm reaches simultaneously a better accuracy in practice compared to previously known such fast algorithms, and a time complexity bound with the best currently known leading term (obtained via alternate basis sparsification). To build this algorithm, we consider matrix and tensor norms bounds governing the stability and accuracy of numerical matrix multiplication. First, we reduce those bounds by minimizing a growth factor along the unique orbit of Strassen's 2×2-matrix multiplication tensor decomposition. Second, we develop heuristics for minimizing the number of operations required to realize a given bilinear formula, while further improving its accuracy. Third, we perform an alternate basis sparsification that improves on the time complexity constant and mostly preserves the overall accuracy.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Calcul réparti sécurisé : Cryptographie, Combinatoire, Calcul Formel
IDEX UGA
Cryptanalyse de primitives cryptographiques classiques

Collections :