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 17 articles )

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