论文标题
从其线性化的扰动中恢复矩阵多项式的扰动
Recovering a perturbation of a matrix polynomial from a perturbation of its linearization
论文作者
论文摘要
矩阵多项式的许多理论和计算问题是通过线性化解决的。因此，线性化的扰动理论需要与基质多项式有关。在本文中，我们提出了一种算法，该算法发现矩阵多项式的基质系数的扰动对应于整个线性铅笔的给定扰动。此外，我们发现通过严格的等效性，转化矩阵将线性化的扰动转化为扰动多项式的线性化。为简单起见，我们为第一个伴侣线性化提供了结果，但可以将其推广到更广泛的线性化类别。
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we present an algorithm that finds which perturbation of matrix coefficients of a matrix polynomial corresponds to a given perturbation of the entire linearization pencil. Moreover we find transformation matrices that, via strict equivalence, transform a perturbation of the linearization to the linearization of a perturbed polynomial. For simplicity, we present the results for the first companion linearization but they can be generalized to a broader class of linearizations.
