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Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices
In inverse eigenvalue problems one tries to reconstruct a matrix, satisfying some constraints, given some spectral information. Here, two inverse eigenvalue problems are solved. First, given the eigenvalues and the first components of the associated ...
A unitary Hessenberg QR-based algorithm via semiseparable matrices
In this paper, we present a novel method for solving the unitary Hessenberg eigenvalue problem. In the first phase, an algorithm is designed to transform the unitary matrix into a diagonal-plus-semiseparable form. Then we rely on our earlier adaptation ...
Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank-One Perturbations of Unitary Matrices
Let $\mathcal H_n\subset \mathbb C^{n\times n}$ be the class of $n\times n$ Hessenberg matrices $A$ which are rank-one modifications of a unitary matrix, that is, $A=H +\B u\B w^H$, where $H$ is unitary and $\mathbf{u}, \mathbf{w}\in \mathbb C^n$. The ...
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