Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 837527, 11 pages
Research Article

An Inverse Eigenvalue Problem of Hermite-Hamilton Matrices in Structural Dynamic Model Updating

Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 11 February 2010; Accepted 27 April 2010

Academic Editor: Angelo Luongo

Copyright © 2010 Linlin Zhao and Guoliang Chen. 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 consider the following inverse eigenvalue problem: given XCn×m and a diagonal matrix ΛCm×m, find n×n Hermite-Hamilton matrices K and M such that KX=MXΛ. We then consider an optimal approximation problem: given n×n Hermitian matrices Ka and Ma, find a solution (K,M) of the above inverse problem such that K-Ka2+M-Ma2=min. By using the Moore-Penrose generalized inverse and the singular value decompositions, the solvability conditions and the representations of the general solution for the first problem are derived. The expression of the solution to the second problem is presented.