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.

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  1. Heule, Marijn J. H.; Kauers, Manuel; Seidl, Martina: New ways to multiply (3 \times3)-matrices (2021)
  2. Shoup, Victor: Arithmetic software libraries (2021)
  3. Torrance, Douglas A.; Vannieuwenhoven, Nick: All secant varieties of the Chow variety are nondefective for cubics and quaternary forms (2021)
  4. Hyun, Seung Gyu; Neiger, Vincent; Rahkooy, Hamid; Schost, Éric: Block-Krylov techniques in the context of sparse-FGLM algorithms (2020)
  5. Hyun, Seung Gyu; Neiger, Vincent; Schost, Éric: Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants (2019)
  6. 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)
  7. Abo, Hirotachi; Vannieuwenhoven, Nick: Most secant varieties of tangential varieties to Veronese varieties are nondefective (2018)
  8. Doliskani, Javad; Giorgi, Pascal; Lebreton, Romain; Schost, Eric: Simultaneous conversions with the residue number system using linear algebra (2018)
  9. Cenk, Murat; Hasan, M. Anwar: On the arithmetic complexity of Strassen-like matrix multiplications (2017)
  10. Hyun, Seung Gyu; Lebreton, Romain; Schost, Éric: Algorithms for structured linear systems solving and their implementation (2017)
  11. Pan, Victor Ya.: Fast matrix multiplication and its algebraic neighbourhood (2017)
  12. Eröcal, Burçin; Motsak, Oleksandr; Schreyer, Frank-Olaf; Steenpaß, Andreas: Refined algorithms to compute syzygies (2016)
  13. Harrison, Gavin; Johnson, Jeremy; Saunders, B. David: Probabilistic analysis of Wiedemann’s algorithm for minimal polynomial computation (2016)
  14. Bertolazzi, Enrico; Rimoldi, Anna: Fast matrix decomposition in (\mathbbF_2) (2014)
  15. Cheng, Howard; Labahn, George: A practical implementation of a modular algorithm for ore polynomial matrices (2014)
  16. Dumas, Jean-Guillaume; Pernet, Clément; Sultan, Ziad: Simultaneous computation of the row and column rank profiles (2013)
  17. Jeannerod, Claude-Pierre; Pernet, Clément; Storjohann, Arne: Rank-profile revealing Gaussian elimination and the CUP matrix decomposition (2013)
  18. Ballico, Edoardo; Brambilla, Maria Chiara; Caruso, Fabrizio; Sala, Massimiliano: Postulation of general quintuple fat point schemes in (\mathbbP^3) (2012)
  19. Dureisseix, David: Generalized fraction-free (LU) factorization for singular systems with kernel extraction (2012)
  20. Cook, William; Steffy, Daniel E.: Solving very sparse rational systems of equations (2011)

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