An inverse eigenvalue problem of Hermite-Hamilton matrices in structural dynamic model updating
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.
scientific article; zbMATH DE number 5728520