On a Partially Described Inverse Quadratic Eigenvalue Problem

Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem

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 nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

STRUCTURED QUADRATIC INVERSE EIGENVALUE PROBLEM , I . SERIALLY LINKED SYSTEMS DRAFT AS OF October 16 , 2006

Quadratic pencils arising from applications are often inherently structured. Factors contributing to the structure include the connectivity of elements within the underlying physical system and the mandatory nonnegativity of physical parameters. For physical feasibility, structural constraints must be respected. Consequently, they impose additional challenges on the inverse eigenvalue problems ...

On Inverse Quadratic Eigenvalue Problems with Partially Prescribed Eigenstructure

The inverse eigenvalue problem of constructing real and symmetric square matrices M , C, and K of size n × n for the quadratic pencil Q(λ) = λ2M + λC + K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is considered. This paper consists of two parts addressing two related but different problems. The first part deals with the inverse problem where M and K are required to be ...