LinBox Founding Scope Allocation, Parallel Building Blocks, and Separate Compilation

  • Jean-Guillaume Dumas
  • Thierry Gautier
  • Clément Pernet
  • B. David Saunders
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)


As a building block for a wide range of applications, computational exact linear algebra has to conciliate efficiency and genericity. The goal of the LinBox project is to address this problem in the design of an efficient general-purpose C++ opensource library for exact linear algebra over the integers, the rationals, and finite fields. Matrices can be either dense, sparse or black box (i.e. viewed as a linear operator, acting on vectors only). The library proposes a set of high level linear algebra solutions, such as the rank, the determinant, the solution of a linear system, the Smith normal form, the echelon form, the characteristic polynomial, etc.


Computer Algebra System Compilation Time Compilation Model Reference Counting Smith Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Chen, L., Eberly, W., Kaltofen, E., Saunders, B.D., Turner, W.J., Villard, G.: Efficient matrix preconditioners for black box linear algebra. Linear Algebra and its Applications 343-344, 119–146 (2002)Google Scholar
  2. 2.
    Dumas, J.-G., Gautier, T., Giesbrecht, M., Giorgi, P., Hovinen, B., Kaltofen, E., Saunders, B.D., Turner, W.J., Villard, G.: Linbox: A generic library for exact linear algebra. In: ICMS 2002, pp. 40–50 (August 2002)Google Scholar
  3. 3.
    Dumas, J.-G., Gautier, T., Roch, J.-L.: Generic design of chinese remaindering schemes. In: PASCO 2010 (July 2010)Google Scholar
  4. 4.
    Dumas, J.-G., Giorgi, P., Pernet, C.: Dense linear algebra over word-size prime fields: the fflas and ffpack packages. ACM Trans. Math. Softw. 35(3), 1–42 (2008)CrossRefGoogle Scholar
  5. 5.
    Erlingsson, U., Kaltofen, E., Musser, D.: Generic Gram-Schmidt orthogonalization by exact division. In: ISSAC 1996, pp. 275–282 (July 1996)Google Scholar
  6. 6.
    Gautier, T., Besseron, X., Pigeon, L.: KAAPI: a thread scheduling runtime system for data flow computations on cluster of multi-processors. In: PASCO 2007, pp. 15–23 (2007)Google Scholar
  7. 7.
    Kaltofen, E., Morozov, D., Yuhasz, G.: Generic matrix multiplication and memory management in LinBox. In: ISSAC 2005, pp. 216–223 (July 2005)Google Scholar
  8. 8.
    Traore, D., Roch, J.L., Maillard, N., Gautier, T., Bernard, J.: Deque-free work-optimal parallel STL algorithms. In: EUROPAR 2008, Las Palmas, Spain (August 2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jean-Guillaume Dumas
    • 1
  • Thierry Gautier
    • 2
  • Clément Pernet
    • 2
  • B. David Saunders
    • 3
  1. 1.Laboratoire J. KuntzmannUniversité de GrenobleGrenobleFrance
  2. 2.Laboratoire LIGUniversité de Grenoble et INRIA. umr CNRSMontbonnotFrance
  3. 3.Computer and Information Science DepartmentUniversity of DelawareNewarkUSA

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