Spectral approximation of banded Laurent matrices with localized random perturbations
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_{j...
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| Format: | Report |
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Unspecified
2001
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| _version_ | 1826268774915899392 |
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| author | Boettcher, A Embree, M Lindner, M |
| author_facet | Boettcher, A Embree, M Lindner, M |
| author_sort | Boettcher, A |
| collection | OXFORD |
| description | 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 $\Omega$. |
| first_indexed | 2024-03-06T21:14:47Z |
| format | Report |
| id | oxford-uuid:3f66d61c-56cd-4e7b-85f5-875a80a489d3 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:14:47Z |
| publishDate | 2001 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:3f66d61c-56cd-4e7b-85f5-875a80a489d32022-03-26T14:31:51ZSpectral approximation of banded Laurent matrices with localized random perturbationsReporthttp://purl.org/coar/resource_type/c_93fcuuid:3f66d61c-56cd-4e7b-85f5-875a80a489d3Mathematical Institute - ePrintsUnspecified2001Boettcher, AEmbree, MLindner, MThis 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 $\Omega$. |
| spellingShingle | Boettcher, A Embree, M Lindner, M Spectral approximation of banded Laurent matrices with localized random perturbations |
| title | Spectral approximation of banded Laurent matrices with localized random perturbations |
| title_full | Spectral approximation of banded Laurent matrices with localized random perturbations |
| title_fullStr | Spectral approximation of banded Laurent matrices with localized random perturbations |
| title_full_unstemmed | Spectral approximation of banded Laurent matrices with localized random perturbations |
| title_short | Spectral approximation of banded Laurent matrices with localized random perturbations |
| title_sort | spectral approximation of banded laurent matrices with localized random perturbations |
| work_keys_str_mv | AT boettchera spectralapproximationofbandedlaurentmatriceswithlocalizedrandomperturbations AT embreem spectralapproximationofbandedlaurentmatriceswithlocalizedrandomperturbations AT lindnerm spectralapproximationofbandedlaurentmatriceswithlocalizedrandomperturbations |