论文标题
一个和几个变量中矩阵多项式的稳定性
Stability Of Matrix Polynomials In One And Several Variables
论文作者
论文摘要
本文提出了常规基质多项式定位的特征值定位方法，特别是研究基质多项式的稳定性。为此，引入并广泛讨论了更强的高估性概念。显示了高斯 - 卢卡斯定理和szász不平等的基质版本。此外，还提供了通过多元复杂分析方法研究（超级）稳定性的工具。具有对系数的特定半定义假设的几个二阶和三阶矩阵多项式显示为稳定。
The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix versions of the Gauss-Lucas theorem and Szász inequality are shown. Further, tools for investigating (hyper)stability by multivariate complex analysis methods are provided. Several second- and third-order matrix polynomials with particular semi-definiteness assumptions on coefficients are shown to be stable.
