Bibliographic record for `Dumas:2008:DLA'

@Article{Dumas:2008:DLA,
  author =       "Jean-Guillaume Duma and Pascal Giorgi and Cl\'ement Pernet",
  title =        "Dense Linear Algebra over Word-Size Prime Fields: the {FFLAS} and {FFPACK} packages",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "35",
  number =       "3",
  accepted =     "8 February 2008",
  upcoming =     "true",
  abstract =     "In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear 
                 algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide 
                 efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known 
                 that  modular techniques such as the Chinese remainder algorithm or the $p$-adic lifting allow very good practical 
                 performance, especially when word size arithmetic are used. Therefore, finite field arithmetic becomes an important 
                 core for efficient exact linear algebra libraries. In this paper, we study high performance implementations of basic 
                 linear algebra routines over word size prime fields: specially the matrix multiplication; our goal being to provide an 
                 exact alternate to the numerical BLAS library. We show that this is made possible by a careful combination of numerical 
                 computations and asymptotically faster algorithms. Our kernel has several symbolic linear algebra applications enabled 
                 by diverse matrix multiplication reductions: symbolic triangularization, system solving, determinant and matrix inverse 
                 implementations are thus studied",
}