从矩阵多项式线性化的扰动恢复其扰动
Recovering a perturbation of a matrix polynomial from a perturbation of its linearization
摘要：
矩阵多项式的一些理论和计算问题通过线性化来解决。因此，线性化的扰动理论结果需要与矩阵多项式相关。在本文中，我们提出了一种算法，发现其中矩阵多项式的矩阵系数的扰动对应于整个线性化束的给定扰动。此外，我们发现的变换矩阵，通过严格的等价性，将扰动的线性化的线性化的扰动多项式。为了简单起见，我们提出的第一同伴线性化的结果，但它们可以推广到更广泛的一类线性化。
英文摘要：
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.
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