𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Spectral clustering properties of block multilevel Hankel matrices

✍ Scribed by Dario Fasino; Paolo Tilli

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
83 KB
Volume
306
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

By means of recent results concerning spectral distributions of Toeplitz matrices, we show that the singular values of a sequence of block p-level Hankel matrices H n (Β΅), generated by a p-variate, matrix-valued measure Β΅ whose singular part is finitely supported, are always clustered at zero, thus extending a result known when p = 1 and Β΅ is real valued and Lipschitz continuous. The theorems hold for both eigenvalues and singular values; in the case of singular values, we allow the involved matrices to be rectangular.

πŸ“œ SIMILAR VOLUMES

Block diagonalization and LU-equivalence
Block diagonalization and LU-equivalence of Hankel matrices
✍ Nadia Ben Atti; Gema M. Diaz–Toca πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 196 KB

This article presents a new algorithm for obtaining a block diagonalization of Hankel matrices by means of truncated polynomial divisions, such that every block is a lower Hankel matrix. In fact, the algorithm generates a block LU-factorization of the matrix. Two applications of this algorithm are a

Spectral refinement for clustered eigenv
Spectral refinement for clustered eigenvalues of quasi-diagonal matrices
✍ Mario Ahues; Filomena Dias d’Almeida; Alain Largillier; Paulo B. Vasconcelos πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 139 KB

We extend to a general situation the method for the numerical computation of eigenvalues and eigenvectors of a quasi-diagonal matrix, which is based on a perturbed fixed slope Newton iteration, and whose convergence was proved by the authors in a previous paper, under the hypothesis that the diagona