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

Linlin Zhao | Zendy; Guoliang Chen | Zendy

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

Author(s) -

Linlin Zhao,

Guoliang Chen

Publication year - 2010

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2010/837527

Subject(s) - mathematics , hermitian matrix , hermite polynomials , eigenvalues and eigenvectors , inverse , singular value , combinatorics , matrix (chemical analysis) , inverse problem , generalized inverse , diagonal , moore–penrose pseudoinverse , pure mathematics , mathematical analysis , physics , geometry , quantum mechanics , chemistry , chromatography

We first consider the following inverse eigenvalue problem: given X∈Cn×m and a diagonal matrix Λ∈Cm×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-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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