@article{KALTOFEN2004133,
    Abstract = {Computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods. We survey the complexity of existing methods to solve these problems when the input is an n×n matrix A with integer entries. We study the bit-complexities of the algorithms asymptotically in n and the norm of A. Existing approaches rely on numerical approximate computations, on exact computations, or on both types of arithmetic in combination.},
    Author = {Kaltofen, Erich and Villard, Gilles},
    File = {Computing the sign or the value of the determinant of an integer matrix, a complexity survey - 1-s2.0-S0377042703007234-main.pdf},
    ISSN = {0377-0427},
    Journal = {Journal of Computational and Applied Mathematics},
    Keywords = {Determinant, Bit-complexity, Integer matrix, Approximate computation, Exact computation, Randomized algorithms},
    Note = {Proceedings of the International Conference on Linear Algebra and Arithmetic 2001},
    Number = {1},
    Pages = {133-146},
    Title = {Computing the sign or the value of the determinant of an integer matrix, a complexity survey},
    URL = {https://www.sciencedirect.com/science/article/pii/S0377042703007234},
    Volume = {162},
    Year = {2004},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0377042703007234},
    bdsk-url-2 = {https://doi.org/10.1016/j.cam.2003.08.019},
    date-added = {2023-09-21 08:28:23 +0200},
    date-modified = {2023-09-21 08:28:23 +0200},
    doi = {10.1016/j.cam.2003.08.019}
}

@article{KALTOFEN2004133, Abstract = {Computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods. We survey the complexity of existing methods to solve these problems when the input is an n×n matrix A with integer entries. We study the bit-complexities of the algorithms asymptotically in n and the norm of A. Existing approaches rely on numerical approximate computations, on exact computations, or on both types of arithmetic in combination.}, Author = {Kaltofen, Erich and Villard, Gilles}, File = {Computing the sign or the value of the determinant of an integer matrix, a complexity survey - 1-s2.0-S0377042703007234-main.pdf}, ISSN = {0377-0427}, Journal = {Journal of Computational and Applied Mathematics}, Keywords = {Determinant, Bit-complexity, Integer matrix, Approximate computation, Exact computation, Randomized algorithms}, Note = {Proceedings of the International Conference on Linear Algebra and Arithmetic 2001}, Number = {1}, Pages = {133-146}, Title = {Computing the sign or the value of the determinant of an integer matrix, a complexity survey}, URL = {https://www.sciencedirect.com/science/article/pii/S0377042703007234}, Volume = {162}, Year = {2004}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0377042703007234}, bdsk-url-2 = {https://doi.org/10.1016/j.cam.2003.08.019}, date-added = {2023-09-21 08:28:23 +0200}, date-modified = {2023-09-21 08:28:23 +0200}, doi = {10.1016/j.cam.2003.08.019} }