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Ilmonen PHaukkanen P(2011)Smith meets Smith: Smith normal form of Smith matrixLinear and Multilinear Algebra10.1080/0308108100370981959:5(557-564)Online publication date: May-2011
https://doi.org/10.1080/03081081003709819
ALAGAR VROY A(2007)A comparative study of algorithms for computing the Smith normal form of an integer matrix†International Journal of Systems Science10.1080/0020772840892659515:7(727-744)Online publication date: 15-May-2007
https://doi.org/10.1080/00207728408926595
Dumas JDavid Saunders BVillard G(2001)On Efficient Sparse Integer Matrix Smith Normal Form ComputationsJournal of Symbolic Computation10.1006/jsco.2001.045132:1(71-99)Online publication date: 1-Jul-2001
https://dl.acm.org/doi/10.1006/jsco.2001.0451

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On Computing the Smith Normal Form of an Integer Matrix

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A fast algorithm for computing the Smith normal form with multipliers for a nonsingular integer matrix
Abstract
A Las Vegas randomized algorithm is given to compute the Smith multipliers for a nonsingular integer matrix A, that is, unimodular matrices U and V such that A V = U S, with S the Smith normal form of A. The expected running time of ...
On computing the determinant and Smith form of an integer matrix
FOCS '00: Proceedings of the 41st Annual Symposium on Foundations of Computer Science

A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A/spl isin/Z/sup n/spl times/n/ the algorithm requires O(n/sup 3.5/(log n)/sup 4.5/) bit operations (assuming for now that entries in A have ...
A local construction of the Smith normal form of a matrix polynomial

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately ...

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 5, Issue 4

Dec. 1979

153 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/355853

Editor:
John R. Rice

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Association for Computing Machinery

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Published: 01 December 1979

Published in TOMS Volume 5, Issue 4

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Ilmonen PHaukkanen P(2011)Smith meets Smith: Smith normal form of Smith matrixLinear and Multilinear Algebra10.1080/0308108100370981959:5(557-564)Online publication date: May-2011
https://doi.org/10.1080/03081081003709819
ALAGAR VROY A(2007)A comparative study of algorithms for computing the Smith normal form of an integer matrix†International Journal of Systems Science10.1080/0020772840892659515:7(727-744)Online publication date: 15-May-2007
https://doi.org/10.1080/00207728408926595
Dumas JDavid Saunders BVillard G(2001)On Efficient Sparse Integer Matrix Smith Normal Form ComputationsJournal of Symbolic Computation10.1006/jsco.2001.045132:1(71-99)Online publication date: 1-Jul-2001
https://dl.acm.org/doi/10.1006/jsco.2001.0451

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A fast algorithm for computing the Smith normal form with multipliers for a nonsingular integer matrix

On computing the determinant and Smith form of an integer matrix

A local construction of the Smith normal form of a matrix polynomial

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