A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure
A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure
复制标题
具有部分特征结构的二次反特征值问题的对偶优化方法
DOI：
10.1137/060656346
复制
发表时间：
2007-01-01
影响因子：
3.1
通讯作者：
Sun, Defeng
中科院分区：
文献类型：
--
作者：
Bai, Zheng-Jian;Chu, Delin;Sun, Defeng
二次特征值反问题（IQEP）是结构动力学中的一个重要问题.它的目的是找到三个对称矩阵，即质量矩阵、阻尼矩阵和刚度矩阵，使它们最接近给定的分析矩阵并满足测量数据。这一问题的难点在于应用中质量矩阵必须正定，刚度矩阵必须半正定。基于IQEP的一个等价的对偶优化版本，我们提出了一个二次收敛的牛顿型方法。我们的数值实验证实了所提出的方法的高效率。
The inverse quadratic eigenvalue problem (IQEP) arises in the field of structural dynamics. It aims to find three symmetric matrices, known as the mass, the damping, and the stiffness matrices, such that they are closest to the given analytical matrices and satisfy the measured data. The difficulty of this problem lies in the fact that in applications the mass matrix should be positive definite and the stiffness matrix positive semidefinite. Based on an equivalent dual optimization version of the IQEP, we present a quadratically convergent Newton-type method. Our numerical experiments confirm the high efficiency of the proposed method.