In the framework of Polynomial Eigenvalue Problems (PEPs), most matrix polynomials arising in applications are structured (namely, (skew-)symmetric, (skew-)Hermitian, (anti-)palindromic, or alternating). The standard way to solve PEPs is by means linearizations. frequently used linearizations belong general constructions, valid for all a fixed degree, known as companion It well known, however, ...

A matrix S ∈ C2m×2m is symplectic if SJS∗ = J , where J = [ 0 −Im Im 0 ] . Symplectic matrices play an important role in the analysis and numerical solution of matrix problems involving the indefinite inner product x∗(iJ)y. In this paper we provide several matrix factorizations related to symplectic matrices. We introduce a singular value-like decomposition B = QDS−1 for any real matrix B ∈ Rn×...

Most eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can help preserve physically relevant symmetries in the eigenvalues of the matrix and may improve the accuracy and efficiency of an eigenvalue c...

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic var...

Structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations. This paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization, including the classes of real, skew-symmetric, Hermitian, and Hamiltonian perturbations. For all these struc...

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping ...

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping ...

The inverse problems play an important role in MEG reconstructions [3, 4, 5, 6, 7]. In this paper, a partially described inverse eigenvalue problem and an associated optimal approximation problem for J-centrosymmetric matrices are considered respectively. It is shown under which conditions the inverse eigenproblem has a solution. An expression of its general solution is given. In case a solutio...