矩形多项式矩阵的Popov型和Hermite型的计算
Computing Popov and Hermite forms of rectangular polynomial matrices
摘要：
本文研究了一元多项式上矩阵的两种范式：Popov型和Hermite型的计算。对于矩阵的平方和非奇异，确定性算法与满意的成本界是已知的。在这里，我们提出了确定性，快速算法的矩形输入矩阵。所获得的波波夫形式的成本界匹配以前最好的已知的随机算法，而成本界的Hermite形式的改进，以前最好的已知的一个因素，这至少是最大的输入矩阵的维数。
英文摘要：
We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are known. Here, we present deterministic, fast algorithms for rectangular input matrices. The obtained cost bound for the Popov form matches the previous best known randomized algorithm, while the cost bound for the Hermite form improves on the previous best known ones by a factor which is at least the largest dimension of the input matrix.
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