For the nonlinear eigenvalue problem T (λ)x = 0 we consider a Jacobi–Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.

For a graph $G$, we associate family of real symmetric matrices, $\mathcal{S}(G)$, where for any $M \in \mathcal{S}(G)$, the location nonzero off-diagonal entries $M$ is governed by adjacency structure $G$. The ordered multiplicity Inverse Eigenvalue Problem Graph (IEPG) concerned with finding all attainable lists eigenvalue multiplicities matrices in $\mathcal{S}(G)$. connected graphs order si...

The inverse eigenvalue problem of constructing symmetric positive semidefinite matrixD written as D ≥ 0 and real-valued skew-symmetric matrix G i.e., G −G of order n for the quadratic pencilQ λ : λMa λ D G Ka, whereMa > 0,Ka ≥ 0 are given analytical mass and stiffness matrices, so that Q λ has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient condition...