Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems
Given k pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing n×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(λ)=λ2M+λ(D+G)+K has the given k...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/703178 |
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| author | Hong-Xiu Zhong Guo-Liang Chen Xiang-Yun Zhang |
| author_facet | Hong-Xiu Zhong Guo-Liang Chen Xiang-Yun Zhang |
| author_sort | Hong-Xiu Zhong |
| collection | DOAJ |
| description | Given k pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing n×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(λ)=λ2M+λ(D+G)+K has the given k pairs as eigenpairs. First, we construct a general solution to this problem with k≤n. Then, with the special properties D=0 and K<0, we construct a particular solution. Numerical results illustrate these solutions. |
| format | Article |
| id | doaj-art-40a23bb0013f4df699c5882bcffb4c6c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-40a23bb0013f4df699c5882bcffb4c6c2025-02-03T01:09:24ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/703178703178Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order SystemsHong-Xiu Zhong0Guo-Liang Chen1Xiang-Yun Zhang2Department of Mathematics, East China Normal University, Shanghai 200241, ChinaDepartment of Mathematics, East China Normal University, Shanghai 200241, ChinaDepartment of Mathematics, East China Normal University, Shanghai 200241, ChinaGiven k pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing n×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(λ)=λ2M+λ(D+G)+K has the given k pairs as eigenpairs. First, we construct a general solution to this problem with k≤n. Then, with the special properties D=0 and K<0, we construct a particular solution. Numerical results illustrate these solutions.http://dx.doi.org/10.1155/2014/703178 |
| spellingShingle | Hong-Xiu Zhong Guo-Liang Chen Xiang-Yun Zhang Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems Journal of Applied Mathematics |
| title | Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems |
| title_full | Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems |
| title_fullStr | Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems |
| title_full_unstemmed | Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems |
| title_short | Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems |
| title_sort | solutions of a quadratic inverse eigenvalue problem for damped gyroscopic second order systems |
| url | http://dx.doi.org/10.1155/2014/703178 |
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