On Efficient Sparse Integer Matrix Smith Normal Form Computations

@article{Dumas2001OnES,
  title={On Efficient Sparse Integer Matrix Smith Normal Form Computations},
  author={J. Dumas and B. Saunders and G. Villard},
  journal={J. Symb. Comput.},
  year={2001},
  volume={32},
  pages={71-99}
}
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… Expand
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References

SHOWING 1-10 OF 93 REFERENCES
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
  • 253
  • Highly Influential
...
1
2
3
4
5
...