scholarly journals A generalized inverse eigenvalue problem in structural dynamic model updating

2009 ◽  
Vol 226 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Yong-Xin Yuan ◽  
Hua Dai
Keyword(s):  
Eigenvalue Problem ◽  
Dynamic Model ◽  
Generalized Inverse ◽  
Model Updating ◽  
Inverse Eigenvalue Problem ◽  
Structural Dynamic ◽  
Generalized Inverse Eigenvalue Problem ◽  
Structural Dynamic Model ◽  
Inverse Eigenvalue

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

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Linlin Zhao ◽  
Guoliang Chen
Keyword(s):  
Eigenvalue Problem ◽  
Generalized Inverse ◽  
Model Updating ◽  
Approximation Problem ◽  
Inverse Eigenvalue Problem ◽  
Structural Dynamic ◽  
Solvability Conditions ◽  
Structural Dynamic Model ◽  
Singular Value Decompositions ◽  
Inverse Eigenvalue

We first consider the following inverse eigenvalue problem: givenX∈Cn×mand a diagonal matrixΛ∈Cm×m, findn×nHermite-Hamilton matricesKandMsuch thatKX=MXΛ. We then consider an optimal approximation problem: givenn×nHermitian matricesKaandMa, find a solution(K,M)of the above inverse problem such that∥K-Ka∥2+∥M-Ma∥2=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.

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