Asymptotically fast polynomial matrix algorithms for multivariable systems
<|reference_start|>Asymptotically fast polynomial matrix algorithms for multivariable systems: We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer algebra techniques, minimal basis computations and matrix fraction expansion/reconstruction, and to polynomial matrix multiplication. Such reductions eventually imply that all these problems can be solved in about the same amount of time as polynomial matrix multiplication.<|reference_end|>
@article{jeannerod2005asymptotically,
    title={Asymptotically fast polynomial matrix algorithms for multivariable
  systems},
    author={Claude-Pierre Jeannerod (LIP), Gilles Villard (LIP)},
    journal={arXiv preprint arXiv:cs/0508113},
    year={2005},
    number={JeVi05},
    archivePrefix={arXiv},
    eprint={cs/0508113},
    primaryClass={cs.SC cs.CC}
}