多变量系统的渐近快速多项式矩阵算法
Asymptotically fast polynomial matrix algorithms for multivariable systems
摘要：
本文给出了求解一元多项式矩阵秩、零空间、行列式、一般逆、约化形式等基本问题的渐近最快算法。我们表明，它们基本上可以减少到两个计算机代数技术，最小基计算和矩阵分数的扩展/重建，和多项式矩阵乘法。这样的简化最终意味着所有这些问题都可以在与多项式矩阵乘法相同的时间内解决。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
