On large Toeplitz band matrices with an uncertain block
BibTeX
@MISC{Böttcher_onlarge,
author = {A. Böttcher and M. Embree and V.I. Sokolov},
title = {On large Toeplitz band matrices with an uncertain block},
year = {}
}
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Abstract
This report investigates the possible spectra of large, nite dimensional Toeplitz band matrices with perturbations (impurities, uncertainties) in the upper-left mm block. The main result shows that the asymptotic spectrum of such a matrix is not aected by these perturbations, provided they have suciently small norm. This follows from analysis of structured pseudospectra (structured spectral value sets). In contrast, for typical non-Hermitian Toeplitz matrices there exist certain rankone perturbations of arbitrarily small norm that move an eigenvalue away from the asymptotic spectrum in the large-dimensional limit. 1
