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Spectral approximation of banded laurent matrices with localized random perturbations
Publikationstyp
Journal Article
Date Issued
2002-12-03
Sprache
English
Author(s)
Volume
42
Issue
2
Start Page
142
End Page
165
Citation
Integral Equations and Operator Theory 42 (2): 142-165 (2002-12-03)
Publisher DOI
Scopus ID
This paper explores the relationship between the spectra of perturbed infinite banded Laurent matrices L(a) + K and their approximations by perturbed circulant matrices Cn(a) + PnKPn for large n. The entries Kjk of the perturbation matrices assume values in prescribed sets Ωjk at the sites (j, k) of a fixed finite set E, and are zero at the sites (j, k) outside E. With KΩE denoting the ensemble of these perturbation matrices, it is shown that limn→∞ ∪K∈κΩE sp(Cn(a) + PnKPn) = ∪K∈κΩE sp(L(a) + K) under several fairly general assumptions on E and Ω.
DDC Class
510: Mathematik