## Journal of Applied Mathematics

### Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems

#### Abstract

Given $k$ pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing $n{\times}n$ real matrices $M$, $D$, $G$, and $K$, where $M>0$, $K$ and $D$ are symmetric, and $G$ is skew-symmetric, so that the quadratic pencil $Q(\lambda )={\lambda }^{2}M+\lambda (D+G)+K$ has the given $k$ pairs as eigenpairs. First, we construct a general solution to this problem with $k\le n$. Then, with the special properties $D=0$ and $K<0$, we construct a particular solution. Numerical results illustrate these solutions.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 703178, 9 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.jam/1395855289

Digital Object Identifier
doi:10.1155/2014/703178

Mathematical Reviews number (MathSciNet)
MR3166781

Zentralblatt MATH identifier
07010719

#### Citation

Zhong, Hong-Xiu; Chen, Guo-Liang; Zhang, Xiang-Yun. Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems. J. Appl. Math. 2014 (2014), Article ID 703178, 9 pages. doi:10.1155/2014/703178. https://projecteuclid.org/euclid.jam/1395855289

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