Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 730358, 9 pages
An Inverse Quadratic Eigenvalue Problem for Damped Structural Systems
Department of Mathematics, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Received 23 October 2007; Accepted 14 February 2008
Academic Editor: Angelo Luongo
Copyright © 2008 Yongxin Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We first give the representation of the general solution of the following inverse quadratic
eigenvalue problem (IQEP): given
, , and both and are closed under complex conjugation in the sense that , for , and for , find real-valued symmetric -diagonal
matrices , and such that . We then consider an optimal approximation
problem: given real-valued symmetric -diagonal matrices , find such that , where is the solution set of IQEP. We show that the optimal approximation solution is unique and derive an explicit formula for it.