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FOCS
2000
IEEE
13 years 8 months ago
Computing the Determinant and Smith Form of an Integer Matrix
A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A ¡£¢ n¤ n the algorithm requires O¥ n3¦5 ¥ logn§ 4¦5§ bit...
Wayne Eberly, Mark Giesbrecht, Gilles Villard
COCO
2005
Springer
106views Algorithms» more  COCO 2005»
13 years 9 months ago
The Complexity of the Inertia and Some Closure Properties of GapL
The inertia of an n × n matrix A is defined as the triple (i+(A), i−(A), i0(A)), where i+(A), i−(A), and i0(A) are the number of eigenvalues of A, counting multiplicities, w...
Thanh Minh Hoang, Thomas Thierauf
ISAAC
2009
Springer
121views Algorithms» more  ISAAC 2009»
13 years 10 months ago
Generalized Reduction to Compute Toric Ideals
Toric ideals have many applications including solving integer programs. Several algorithms for computing the toric ideal of an integer matrix are available in the literature. Since...
Deepanjan Kesh, Shashank K. Mehta