In this paper, we propose a multi-level finite element method for the transmission eigenvalue problem of anisotropic media. The problem is non-standard and non-self-adjoint with important applications in inverse scattering theory. We employ a suitable finite element method to discretize the problem. The resulting generalized matrix eigenvalue problem is large, sparse and non-Hermitian. To compu...

A list of complex numbers is realizable if it is the spectrum of a nonnegative matrix. In 1949 Sulěımanova posed the nonnegative inverse eigenvalue problem (NIEP): the problem of determining which lists of complex numbers are realizable. The version for reals of the NIEP (RNIEP) asks for realizable lists of real numbers. In the literature there are many sufficient conditions or criteria for lis...

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,...