Asymptotically fast polynomial matrix algorithms for multivariable systems
符号计算
2007-05-23 v1 计算复杂性
摘要
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.
引用
@article{arxiv.cs/0508113,
title = {Asymptotically fast polynomial matrix algorithms for multivariable systems},
author = {Claude-Pierre Jeannerod and Gilles Villard},
journal= {arXiv preprint arXiv:cs/0508113},
year = {2007}
}