The Mathematical Institute, University of Oxford, Eprints Archive

Spectral approximation of banded Laurent matrices with localized random perturbations

Boettcher, A. and Embree, Mark and Lindner, M. (2001) Spectral approximation of banded Laurent matrices with localized random perturbations. Technical Report. Unspecified. (Submitted)

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Abstract

This paper explores the relationship between the spectra of perturbed infinite banded Laurent matrices $L(a)+K$ and their approximations by perturbed circulant matrices $C_{n}(a)+P_{n}KP_{n}$ for large $n$. The entries $K_{jk}$ of the perturbation matrices assume values in prescribed sets $\Omega_{jk}$ at the sites $(j,k)$ of a fixed set $E$, and are zero at the sites $(j,k)$ outside $E$. With ${\cal K}_{\Omega}^{E}$ denoting the ensemble of these perturbation matrices, it is shown that
$\displaystyle\lim_{n\to\infty} 
\displaystyle\bigcup_{K\in{\cal K}_{\Omega}^{E}}
sp(C_{n}(a)+P_{n}KP_{n})=
\displaystyle\bigcup_{K\in{\cal K}_{\Omega}^{E}}
sp(L(a)=K)$
under several fairly general assumptions on $E$ and $\Omega$.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1250
Deposited By:Lotti Ekert
Deposited On:21 May 2011 17:07
Last Modified:21 May 2011 17:07

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