@article{ZHOU2015162,
    Abstract = {Improved cost estimates are given for the problem of computing the inverse of an n×n matrix of univariate polynomials over a field. A deterministic algorithm is demonstrated that has worst case complexity (n3s)1+o(1) field operations, where s≥1 is an upper bound for the average column degree of the input matrix. Here, the ``+o(1)'' in the exponent indicates a missing factor c1(logns)c2 for positive real constants c1 and c2. As an application we show how to compute the largest invariant factor of the input matrix in (n{$\omega$}s)1+o(1) field operations, where {$\omega$} is the exponent of matrix multiplication.},
    Author = {Zhou, Wei and Labahn, George and Storjohann, Arne},
    File = {A deterministic algorithm for inverting a polynomial matrix - 1-s2.0-S0885064X14001009-main - a - y.pdf},
    ISSN = {0885-064X},
    Journal = {Journal of Complexity},
    Keywords = {Polynomial matrix, Matrix inversion, Deterministic algorithm, Nearly optimal algorithm},
    Number = {2},
    Pages = {162 - 173},
    Title = {A deterministic algorithm for inverting a polynomial matrix},
    URL = {http://www.sciencedirect.com/science/article/pii/S0885064X14001009},
    Volume = {31},
    Year = {2015},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0885064X14001009},
    bdsk-url-2 = {https://doi.org/10.1016/j.jco.2014.09.004},
    date-added = {2020-06-10 09:31:41 +0200},
    date-modified = {2020-06-10 09:31:41 +0200},
    doi = {10.1016/j.jco.2014.09.004}
}

@article{ZHOU2015162, Abstract = {Improved cost estimates are given for the problem of computing the inverse of an n×n matrix of univariate polynomials over a field. A deterministic algorithm is demonstrated that has worst case complexity (n3s)1+o(1) field operations, where s≥1 is an upper bound for the average column degree of the input matrix. Here, the ``+o(1)'' in the exponent indicates a missing factor c1(logns)c2 for positive real constants c1 and c2. As an application we show how to compute the largest invariant factor of the input matrix in (n{$\omega$}s)1+o(1) field operations, where {$\omega$} is the exponent of matrix multiplication.}, Author = {Zhou, Wei and Labahn, George and Storjohann, Arne}, File = {A deterministic algorithm for inverting a polynomial matrix - 1-s2.0-S0885064X14001009-main - a - y.pdf}, ISSN = {0885-064X}, Journal = {Journal of Complexity}, Keywords = {Polynomial matrix, Matrix inversion, Deterministic algorithm, Nearly optimal algorithm}, Number = {2}, Pages = {162 - 173}, Title = {A deterministic algorithm for inverting a polynomial matrix}, URL = {http://www.sciencedirect.com/science/article/pii/S0885064X14001009}, Volume = {31}, Year = {2015}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0885064X14001009}, bdsk-url-2 = {https://doi.org/10.1016/j.jco.2014.09.004}, date-added = {2020-06-10 09:31:41 +0200}, date-modified = {2020-06-10 09:31:41 +0200}, doi = {10.1016/j.jco.2014.09.004} }