Eigenvalue problem of Hamiltonian operator matrices

On the nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

on the nonnegative inverse eigenvalue problem of traditional matrices

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

The inverse eigenvalue problem via orthogonal matrices

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvec...

Perturbation theory for Hamiltonian operator matrices and Riccati equations

A rational SHIRA method for the Hamiltonian eigenvalue problem

The complete list of CSC and SFB393 preprints is available via Abstract The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamilto-nian eigenproblems by considering a suitable transformation. Structure-induced shift-and-invert techniques are employed to steer the algo...