Inverse Eigenvalue Problem with Non-simple Eigenvalues for Damped Vibration Systems - Moghadam, M. Mohseni; Tajaddini, A. (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) (λ^2M +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 linear pencils, 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.