In this literature, the symmetric inverse generalized eigenvalue problem with submatrix constraints and its corresponding optimal approximation problem are studied. A necessary and sufficient condition for solvability is derived, and when solvable, the general solutions are presented.

For the nonlinear eigenvalue problem T (λ)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem gover...

Quadratic pencils arise in many areas of important applications. The underlying physical systems often impose inherent structures, which include the predetermined inner-connectivity among elements within the physical system and the mandatory nonnegativity of physical parameters, on the pencils. In the inverse problem of reconstructing a quadratic pencil from prescribed eigeninformation, respect...

We present a real symmetric tridiagonalmatrix of order nwhose eigenvalues are {2k}n−1 k=0 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l + 1}n−2 l=0 . Thematrix entries are explicit functions of the size n, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution ...

This paper presents a brief review of recent developments on quadratic inverse eigenvalue problem with applications to active vibration control and finite element model updating.

We present different stability estimates for the Jacobi inverse eigenvalue problem. First, we give upper bounds expressed in terms of quadrature data and not having weights in denominators. The technique of orthonormal polynomials and integral representation of Hankel determinants is used. Our bounds exhibit only polynomial growth in the problem’s dimension (see [4]). It has been shown that the...

In this paper, we discuss the solution of an Inverse Eigenvalue Complementarity Problem. Two nonlinear formulations are presented for this problem. A necessary and sufficient condition for a stationary point of the first of these formulations to be a solution of the problem is established. On the other hand, for assuring global convergence to a solution of this problem when it exists, an enumer...

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 ...

Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Z be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Z such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Z is an affine variety over an algebraically closed field.