In [1] the recursive inverse eigenvalue problem for matrices was introduced. In this paper we examine an open problem on the existence of symmetric positive semidefinite solutions that was posed there. We first give several counterexamples for the general case and then characterize under which further assumptions the conjecture is valid. 1. Introduction. In [1] several classes of recursive inve...

A partially described inverse eigenvalue problem and an associated optimal approximation problem for generalized K-centrohermitian matrices are considered. It is shown under which conditions the inverse eigenproblem has a solution. An expression of its general solution is given. In case a solution of the inverse eigenproblem exists, the optimal approximation problem can be solved. The formula o...

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this pape...

This paper discusses the constructional problem for a class of spring-mass systems whose part particles are connected to the ground. The problem is converted to an inverse eigenvalue problem for Jacobi matrix. An inverse eigenvalue problem of determining the system from its some physical parameters and incomplete eigenpairs is solved. The necessary and sufficient condition for constructing the ...