On Parameterised Quadratic Inverse Eigenvalue Problem

被引：2

作者：

Xiang, Meiling ^{[1
]}

Dai, Hua ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2022年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Quadratic inverse eigenvalue problem; multiparameter eigenvalue problem; smooth QR-decomposition; Newton method; NUMERICAL-METHODS; ALGORITHM; MATRICES;

D O I：

10.4208/eajam.250321.230821

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that if prescribed eigenvalues are distinct, then the parameterised quadratic inverse eigenvalue problem is equivalent to a multiparameter eigenvalue problem. Moreover, a sufficient condition for the problem solvability is established. In order to find approximate solution of this problem, we employ the Newton method based on the smooth QR-decomposition with column pivoting and prove its locally quadratic convergence. Numerical examples illustrate the effectiveness of the method. AMS subject classifications: 65F15 Key words: Quadratic inverse eigenvalue problem, multiparameter eigenvalue problem, smooth

引用

页码：185 / 200

页数：16

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