• Matrix multiplication over wor...

Treffer: Matrix multiplication over word-size modular rings using approximate formulae

Title:
Matrix multiplication over word-size modular rings using approximate formulae
Authors:
Boyer, Brice, Dumas, Jean-Guillaume
Contributors:
Department of mathematics North Carolina, North Carolina State University Raleigh (NC State), University of North Carolina System (UNC)-University of North Carolina System (UNC), Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes 2016-2019 (UGA 2016-2019 )-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes 2016-2019 (UGA 2016-2019 ), ANR-11-BS02-0013,HPAC,Calcul Algébrique Haute-Performance(2011)
Source:
ISSN: 0098-3500 ; ACM Transactions on Mathematical Software ; https://hal.science/hal-00987812 ; ACM Transactions on Mathematical Software, 2016, 42 (3-20), ⟨10.1145/2829947⟩.
Publisher Information:
CCSD
Association for Computing Machinery
Publication Year:
2016
Subject Terms:
memory placement and scheduling, symbolic-numeric computing, Bini's approximate bilinear algorithm, Strassen-Winograd's algorithm, efficient implementation, matrix multiplication, exact linear algebra, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Document Type:
Fachzeitschrift article in journal/newspaper
Language:
English
DOI:
10.1145/2829947
Availability:
https://hal.science/hal-00987812
https://hal.science/hal-00987812v1/document
https://hal.science/hal-00987812v1/file/14_bini_matmul_free.pdf
https://doi.org/10.1145/2829947
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edsbas.8337ECDC
Database:
BASE

Weitere Informationen

International audience ; Bini–Capovani–Lotti–Romani approximate formula (or border rank) for matrix multiplication achieves abetter complexity than Strassen’s matrix multiplication formula. In this paper, we show a novel way touse the approximate formula in the special case where the ring is Z/pZ. Besides, we show an implementation à la FFLAS–FFPACK, where p is a word-size modulo, that improves on state-of-the-art Z/pZ matrix multiplication implementations.