Solutions to a quadratic inverse eigenvalue problem

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 ...

Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem

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....

General Solutions for a Class of Inverse Quadratic Eigenvalue Problems

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where n× n real symmetric matrices M , C and K are constructed so that the quadratic pencil Q(λ) = λM + λC + K yields good approximations for the given k eigenpairs. We discuss the case where M is positive definite for 1≤ k ≤ n, and a general solution to this problem for...

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,...