On Efficient Sparse Integer Matrix Smith Normal Form Computations

  title={On Efficient Sparse Integer Matrix Smith Normal Form Computations},
  author={Jean-Guillaume Dumas and B. Saunders and G. Villard},
  journal={J. Symb. Comput.},
  • Jean-Guillaume Dumas, B. Saunders, G. Villard
  • Published 2001
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo powers of word-size primes. Consequently, the algorithm does not suffer from coefficient growth. We have implemented several variants of this algorithm (elimination and/or black box techniques) since practical performance depends strongly on the memory available. Our method has proven useful in… CONTINUE READING
    89 Citations

    Figures, Tables, and Topics from this paper

    Efficient computation of the characteristic polynomial
    • 34
    • PDF
    Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
    • 79
    • PDF
    Computing the Rank of Large Sparse Matrices over Finite Fields
    • 16
    • PDF
    Finite field linear algebra subroutines
    • 86
    • PDF
    Sheafhom: Software for Sparse Integer Matrices
    • PDF
    Bounds on the coefficients of the characteristic and minimal polynomials
    • 5
    • PDF
    Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
    • 66
    • PDF


    Parallel algorithms for matrix normal forms
    • 80
    • PDF
    Probabilistic Computation of the Smith Normal Form of a Sparse Integer Matrix
    • 28
    • Highly Influential
    • PDF
    Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
    • 410
    • PDF
    Near optimal algorithms for computing Smith normal forms of integer matrices
    • 139
    • PDF
    Efficient parallel solution of sparse systems of linear diophantine equations
    • 21
    • Highly Influential
    • PDF
    Algorithms for matrix canonical forms
    • 221
    Effective polynomial computation
    • R. Zippel
    • Mathematics, Computer Science
    • The Kluwer international series in engineering and computer science
    • 1993
    • 252
    • Highly Influential