On an eigenvector-dependent nonlinear eigenvalue problem from the perspective of relative perturbation theory
On an eigenvector-dependent nonlinear eigenvalue problem from the perspective of relative perturbation theory
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DOI：
10.1016/j.cam.2021.113596
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
N. Truhar;Ren-Cang Li
中科院分区：
文献类型：
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作者：
N. Truhar;Ren-Cang Li
我们关注特征向量相关的非线性特征值问题 (NEPv) H (V) V= V Λ，其中 H (V)ε ℂ n× n 是 V ε ℂ n× k 的埃尔米特矩阵值函数，具有正交列，即 V H V= I k，k≤ n（通常 k≪ n）。基于相对微扰理论的众所周知的结果，获得了 NEPv 可解性和解唯一性的充分条件。这些结果是对 Cai 等人（2018）最近的结果的补充，其中，除其他外，我们可以根据绝对微扰理论的众所周知的结果找到 NEPv 的可解性和解唯一性的条件。尽管绝对摄动理论在应用中更通用，但在某些情况下相对摄动理论会产生更好的结果。
We are concerned with the eigenvector-dependent nonlinear eigenvalue problem (NEPv) H (V) V= V Λ, where H (V)∈ ℂ n× n is a Hermitian matrix-valued function of V∈ ℂ n× k with orthonormal columns, ie, V H V= I k, k≤ n (usually k≪ n). Sufficient conditions on the solvability and solution uniqueness of NEPv are obtained, based on the well-known results from the relative perturbation theory. These results are complementary to recent ones in Cai et al.(2018), where, among others, one can find conditions for the solvability and solution uniqueness of NEPv, based on the well-known results from the absolute perturbation theory. Although the absolute perturbation theory is more versatile in applications, there are cases where the relative perturbation theory produces better results.