An Inverse Eigenvalue Problem of Hermite-Hamilton Matrices in Structural Dynamic Model Updating. (28th June 2010)

• Record Type: Journal Article
• Authors: Zhao, Linlin; Chen, Guoliang
• Other Names: Luongo Angelo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010-06-28
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/837527
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We first consider the following inverse eigenvalue problem: given X ∈ C n × m and a diagonal matrix Λ ∈ C m × m, find n × n Hermite-Hamilton matrices K and M such that K X = M X Λ . We then consider an optimal approximation problem: given n × n Hermitian matrices K a and M a, find a solution ( K, M ) of the above inverse problem such that ∥ K - K a ∥ 2 + ∥ M - M a ∥ 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.