About: Deterministic Verification of Integer Matrix Multiplication in Quadratic Time     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

AttributesValues
rdf:type
Description
  • Let A, B and C be n x n matrices of integer numbers. We show that there is a deterministic algorithm of quadratic time complexity (w.r.t. the number of arithmetical operations) verifying whether AB=C. For the integer matrices this result improves upon the best known result by Freivalds from 1977 that only holds for a randomized (Monte Carlo) algorithm. As a consequence, we design a quadratic time nondeterministic integer and rational matrix multiplication algorithm whose time complexity cannot be further improved. This indicates that any technique for proving a super-quadratic lower bound for deterministic matrix multiplication must exploit methods which would not work for the non-deterministic case.
  • Let A, B and C be n x n matrices of integer numbers. We show that there is a deterministic algorithm of quadratic time complexity (w.r.t. the number of arithmetical operations) verifying whether AB=C. For the integer matrices this result improves upon the best known result by Freivalds from 1977 that only holds for a randomized (Monte Carlo) algorithm. As a consequence, we design a quadratic time nondeterministic integer and rational matrix multiplication algorithm whose time complexity cannot be further improved. This indicates that any technique for proving a super-quadratic lower bound for deterministic matrix multiplication must exploit methods which would not work for the non-deterministic case. (en)
Title
  • Deterministic Verification of Integer Matrix Multiplication in Quadratic Time
  • Deterministic Verification of Integer Matrix Multiplication in Quadratic Time (en)
skos:prefLabel
  • Deterministic Verification of Integer Matrix Multiplication in Quadratic Time
  • Deterministic Verification of Integer Matrix Multiplication in Quadratic Time (en)
skos:notation
  • RIV/67985807:_____/14:00425985!RIV14-GA0-67985807
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • I, P(GAP202/10/1333)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 10881
http://linked.open...ai/riv/idVysledku
  • RIV/67985807:_____/14:00425985
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • matrix multiplication; verification of matrix product; Freivald's algorithm (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [9A58413DB9A8]
http://linked.open...v/mistoKonaniAkce
  • Nový Smokovec
http://linked.open...i/riv/mistoVydani
  • Cham
http://linked.open...i/riv/nazevZdroje
  • SOFSEM 2014. Theory and Practice of Computer Science
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Wiedermann, Jiří
  • Korec, I.
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
issn
  • 0302-9743
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/978-3-319-04298-5_33
http://purl.org/ne...btex#hasPublisher
  • Springer-Verlag
https://schema.org/isbn
  • 978-3-319-04297-8
Faceted Search & Find service v1.16.118 as of Jun 21 2024


Alternative Linked Data Documents: ODE     Content Formats:   [cxml] [csv]     RDF   [text] [turtle] [ld+json] [rdf+json] [rdf+xml]     ODATA   [atom+xml] [odata+json]     Microdata   [microdata+json] [html]    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software