An inverse eigenvalue problem of Hermite-Hamilton matrices in structural dynamic model updating
type: Item
instance of: scholarly article
title: An inverse eigenvalue problem of Hermite-Hamilton matrices in structural dynamic model updating
zbMATH Open document ID: 1192.15002
DOI: 10.1155/2010/837527
author: Linlin Zhao
author: Guoliang Chen
published in: Mathematical Problems in Engineering
publication date: 2010-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/228501
review text: Summary: We first consider the following inverse eigenvalue problem: given \(X\in \mathbb C^{n\times m}\) and a diagonal matrix \(\Lambda \in \mathbb C^{^{m\times m}}\), find \(n\times n\) Hermite-Hamilton matrices \(K\) and \(M\) such that \(KX=MX\Lambda \). We then consider an optimal approximation problem: given \(n\times n\) 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.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5728520
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: Hermite-Hamilton matrices
zbMATH Keywords: optimal approximation
zbMATH Keywords: Moore-Penrose generalized inverse
zbMATH Keywords: singular value decompositions
Wikidata QID: Q58653375
MaRDI profile type: Publication
OpenAlex ID: W1987913704
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description: scientific article; zbMATH DE number 5728520