Fraction-free row reduction of matrices of Ore polynomials
Fraction-free row reduction of matrices of Ore polynomials
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Ore 多项式矩阵的无分数行约简
DOI：
10.1016/j.jsc.2005.10.002
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
G. Labahn
中科院分区：
文献类型：
--
作者：
B. Beckermann;Howard Cheng;G. Labahn
本文给出了Ore多项式矩阵行约简的无分式公式。这些约简可用于求这类矩阵的秩和左零空间。当专门为矩阵的斜多项式，我们的减少可以用于计算一个弱波波夫形式的这种矩阵和计算GCRD和LCLM的斜多项式或矩阵的斜多项式。该算法适用于精确算术域中的计算，其中中间计算中的系数的增长是一个问题。该系数增长通过使用无分数方法来控制。已知因素可以被有效地预测和去除。
In this paper we give formulas for performing row reduction of a matrix of Ore polynomials in a fraction-free way. The reductions can be used for finding the rank and left nullspace of such matrices. When specialized to matrices of skew polynomials our reduction can be used for computing a weak Popov form of such matrices and for computing a GCRD and an LCLM of skew polynomials or matrices of skew polynomials. The algorithm is suitable for computation in exact arithmetic domains where the growth of coefficients in intermediate computations is a concern. This coefficient growth is controlled by using fraction-free methods. The known factor can be predicted and removed efficiently.