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Asymptotically fast polynomial matrix algorithms for multivariable systems

Claude-Pierre Jeannerod·Gilles Villard
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Abstract

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.

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Claude-Pierre Jeannerod, Gilles Villard. 2005-08-25. Asymptotically fast polynomial matrix algorithms for multivariable systems. https://arxiv.org/abs/cs/0508113

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