FFPACK: finite field linear algebra package. The FFLAS project has established that exact matrix multiplication over finite fields can be performed at the speed of the highly optimized numerical BLAS routines. Since many algorithms have been reduced to use matrix multiplication in order to be able to prove an optimal theoretical complexity, this paper shows that those optimal complexity algorithms, such as LSP factorization, rank determinant and inverse computation can also be the most efficient.

References in zbMATH (referenced in 20 articles )

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  1. Hyun, Seung Gyu; Neiger, Vincent; Rahkooy, Hamid; Schost, Éric: Block-Krylov techniques in the context of sparse-FGLM algorithms (2020)
  2. Menini, Laura; Possieri, Corrado; Tornambè, Antonio: A linear algebra method to decompose forms whose length is lower than the number of variables into weighted sum of squares (2019)
  3. Abo, Hirotachi; Vannieuwenhoven, Nick: Most secant varieties of tangential varieties to Veronese varieties are nondefective (2018)
  4. Cenk, Murat; Hasan, M. Anwar: On the arithmetic complexity of Strassen-like matrix multiplications (2017)
  5. Pan, Victor Ya.: Fast matrix multiplication and its algebraic neighbourhood (2017)
  6. Eröcal, Burçin; Motsak, Oleksandr; Schreyer, Frank-Olaf; Steenpaß, Andreas: Refined algorithms to compute syzygies (2016)
  7. Harrison, Gavin; Johnson, Jeremy; Saunders, B. David: Probabilistic analysis of Wiedemann’s algorithm for minimal polynomial computation (2016)
  8. Bertolazzi, Enrico; Rimoldi, Anna: Fast matrix decomposition in (\mathbbF_2) (2014)
  9. Cheng, Howard; Labahn, George: A practical implementation of a modular algorithm for ore polynomial matrices (2014)
  10. Dumas, Jean-Guillaume; Pernet, Clément; Sultan, Ziad: Simultaneous computation of the row and column rank profiles (2013)
  11. Jeannerod, Claude-Pierre; Pernet, Clément; Storjohann, Arne: Rank-profile revealing Gaussian elimination and the CUP matrix decomposition (2013)
  12. Ballico, Edoardo; Brambilla, Maria Chiara; Caruso, Fabrizio; Sala, Massimiliano: Postulation of general quintuple fat point schemes in (\mathbbP^3) (2012)
  13. Dureisseix, David: Generalized fraction-free (LU) factorization for singular systems with kernel extraction (2012)
  14. Cook, William; Steffy, Daniel E.: Solving very sparse rational systems of equations (2011)
  15. Dumas, Jean-Guillaume; Fousse, Laurent; Salvy, Bruno: Simultaneous modular reduction and Kronecker substitution for small finite fields (2011)
  16. Böhning, Christian; Graf von Bothmer, Hans-Christian; Kröker, Jakob: Rationality of moduli spaces of plane curves of small degree (2009)
  17. Dumas, Jean-Guillaume; Giorgi, Pascal; Pernet, Clément: Dense linear algebra over word-size prime fields: The FFLAS and FFPACK packages. (2008) ioport
  18. Dumas, Jean-Guillaume; Gautier, Thierry; Giorgi, Pascal; Pernet, Clément: Dense linear algebra over finite fields: The FFLAS and FFPACK packages (2006) ioport
  19. Dumas, Jean-Guillaume; Giorgi, Pascal; Pernet, Clément: FFPACK: finite field linear algebra package (2004)
  20. Gutierrez, Jaime (ed.): Proceedings of the 2004 international symposium on symbolic and algebraic computation, ISSAC 2004, Santander, Spain, July 4--7, 2004 (2004)