Inverse Eigenvalue Problem with Non-simple Eigenvalues for Damped Vibration Systems (Journal of Informatics and Mathematical Sciences, 2009)
In this paper, we will present a general form of real and symmetric $n× n$ matrices $M$, $C$ and $K$ for a quadratic inverse eigenvalue problem QIEP: $Q(λ) \equiv (λ^{2}M +λ C+K) x=0$, so that $Q(λ)$ has a prescribed set of $k$ eigenvalues with algebraic multiplicity $n_{i}$, $i=1,…,k$ which $2n_{1}+2n_{2}+…+2n_{l} +n_{l+1}+…+n_{k}=2n)$. This paper generalizes the method of inverse problem for self-adjoint linearpencils, to self-adjoint quadratic pencils $Q(λ)$. It is shown that this inverse problem involves certain free parameters. Via appropriate choice of free variables in the general form of QIEP, we solve a QIEP.
Keywords: Inverse problem; Quadratic form; Non-simple eigenvalues