Asymptotic Spectra of Dense Toeplitz Matrices Are Unstable

Asymptotic Spectra of Dense Toeplitz Matrices Are Unstable

The paper is concerned with the limiting set of the eigenvalues of the truncations of an infinite Toeplitz matrix whose symbol is continuous but not rational. This limiting set is shown to be unstable with respect to small perturbations of the symbol in the uniform norm, which reveals that the numer...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Numerical algorithms 2003-08, Vol.33 (1-4), p.105-112
Hauptverfasser: Böttcher, A, Grudsky, S.M
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Constraining
Eigenvalues
Mathematical analysis
Numerical analysis
Spectra
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The paper is concerned with the limiting set of the eigenvalues of the truncations of an infinite Toeplitz matrix whose symbol is continuous but not rational. This limiting set is shown to be unstable with respect to small perturbations of the symbol in the uniform norm, which reveals that the numerical computation of the asymptotic spectra of dense Toeplitz matrices is a genuine mathematical challenge.
ISSN:1017-1398
1572-9265
DOI:10.1023/A:1025547501771