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

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.