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Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices
arXiv - CS - Numerical Analysis Pub Date : 2020-07-02 , DOI: arxiv-2007.01188
A.C.M. Ran and Michal Wojtylak

General properties of eigenvalues of $A+\tau uv^*$ as functions of $\tau\in\Comp$ or $\tau\in\Real$ or $\tau=\e^{\ii\theta}$ on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with $\tau\to\infty$ are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex $H$-selfadjoint and real $J$-Hamiltonian.

中文翻译:

非结构化矩阵和结构化矩阵的参数秩一扰动特征值的全局属性

$A+\tau uv^*$ 作为 $\tau\in\Comp$ 或 $\tau\in\Real$ 或 $\tau=\e^{\ii\theta}$ 的函数的特征值的一般性质考虑单位圆。特别是解决了存在特征值的全局解析公式的问题。此外,详细讨论了 $\tau\to\infty$ 的特征值的极限。考虑了以下几类矩阵:复数(无附加结构)、实数(无附加结构)、复数 $H$-selfadjoint 和实数 $J$-Hamiltonian。
更新日期:2020-07-03
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