Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem

Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem

On a Partially Described Inverse Quadratic Eigenvalue Problem

The inverse eigenvalue problem of constructing square matrices M,C and K of size n for the quadratic pencil Q(λ) ≡ λM + λC +K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is considered. This paper offers a constructive proof showing that, given any k ≤ n distinct eigenvalues and linearly independent eigenvectors, the problem is solvable even under the restriction that M,...

Solutions to a quadratic inverse eigenvalue problem

In this paper, we consider the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M,C, and K of size n× n, with (M,C,K) / = 0, so that the quadratic matrix polynomial Q(λ) = λ2M + λC +K has m (n < m 2n) prescribed eigenpairs. It is shown that, for almost all prescribed eigenpairs, the QIEP has a solution with M nonsingular if m < m∗, and has only solutions with ...

On a General Solution of Partially Described Inverse Quadratic Eigenvalue Problems and Its Applications

In this paper, we consider to solve a general form of real and symmetric n× n matrices M , C, K with M being positive definite for an inverse quadratic eigenvalue problem (IQEP): Q(λ)x ≡ (λ2M + λC +K)x = 0, so that Q(λ) has a partially prescribed subset of k eigenvalues and eigenvectors (k ≤ n). Via appropriate choice of free variables in the general form of IQEP, for k = n: we solve (i) an IQE...

On the Inverse Symmetric Quadratic Eigenvalue Problem

The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector data and sign characteristics for the real eigenvalues....