The Mathematical Institute, University of Oxford, Eprints Archive

On large Toeplitz band matrices with an uncertain block

Boettcher, A. and Embree, Mark and Sokolov, V. I. (2001) On large Toeplitz band matrices with an uncertain block. Technical Report. Unspecified. (Submitted)



This report investigates the possible spectra of large, finite dimensional Toeplitz band matrices with perturbations (impurities, uncertainties) in the upper-left m x m block. The main result shows that the asymptotic spectrum of such a matrix is not affected by these perturbations, provided they have sufficiently small norm. This follows from analysis of structured pseudospectra (structured spectral value sets). In contrast, for typical non-Hermitian Toeplitz matrices there exist certain rank-one perturbations of arbitrarily small norm that move an eigenvalue away from the asymptotic spectrum in the large-dimensional limit.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1243
Deposited By: Lotti Ekert
Deposited On:20 May 2011 08:19
Last Modified:29 May 2015 18:56

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