Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds
In this paper, a new upper bound and a new lower bound for the spectral radius of a nοnnegative matrix are proved by using similarity transformations. These bounds depend only on the elements of the nonnegative matrix and its row sums and are compared to the well-established upper and lower Frobeniu...
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ftnkunivathens:oai:lib.uoa.gr:uoadl:3035277 2024-02-11T10:06:23+01:00 Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds Adam, M. Assimakis, N. Babouklis, F. 2020-01-01 https://pergamos.lib.uoa.gr/uoa/dl/object/uoadl:3035277 Αγγλικά English eng uoadl:3035277 https://pergamos.lib.uoa.gr/uoa/dl/object/uoadl:3035277 scientific_publication_article Επιστημονική δημοσίευση - Άρθρο Περιοδικού Scientific publication - Journal Article 2020 ftnkunivathens 2024-01-18T18:35:09Z In this paper, a new upper bound and a new lower bound for the spectral radius of a nοnnegative matrix are proved by using similarity transformations. These bounds depend only on the elements of the nonnegative matrix and its row sums and are compared to the well-established upper and lower Frobenius’ bounds. The proposed bounds are always sharper or equal to the Frobenius’ bounds. The conditions under which the new bounds are sharper than the Frobenius' ones are determined. Illustrative examples are also provided in order to highlight the sharpness of the proposed bounds in comparison with the Frobenius’ bounds. An application to linear invariant discrete-time nonnegative systems is given and the stability of the systems is investigated. The proposed bounds are computed with complexity O(n2). © 2020, North Atlantic University Union. All rights reserved. Article in Journal/Newspaper North Atlantic Pergamos - Library and Information Center of National and Kapodistrian University of Athens |
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Open Polar |
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Pergamos - Library and Information Center of National and Kapodistrian University of Athens |
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ftnkunivathens |
language |
English |
description |
In this paper, a new upper bound and a new lower bound for the spectral radius of a nοnnegative matrix are proved by using similarity transformations. These bounds depend only on the elements of the nonnegative matrix and its row sums and are compared to the well-established upper and lower Frobenius’ bounds. The proposed bounds are always sharper or equal to the Frobenius’ bounds. The conditions under which the new bounds are sharper than the Frobenius' ones are determined. Illustrative examples are also provided in order to highlight the sharpness of the proposed bounds in comparison with the Frobenius’ bounds. An application to linear invariant discrete-time nonnegative systems is given and the stability of the systems is investigated. The proposed bounds are computed with complexity O(n2). © 2020, North Atlantic University Union. All rights reserved. |
format |
Article in Journal/Newspaper |
author |
Adam, M. Assimakis, N. Babouklis, F. |
spellingShingle |
Adam, M. Assimakis, N. Babouklis, F. Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
author_facet |
Adam, M. Assimakis, N. Babouklis, F. |
author_sort |
Adam, M. |
title |
Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
title_short |
Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
title_full |
Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
title_fullStr |
Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
title_full_unstemmed |
Sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
title_sort |
sharp bounds on the spectral radius of nonnegative matrices and comparison to the frobenius’ bounds |
publishDate |
2020 |
url |
https://pergamos.lib.uoa.gr/uoa/dl/object/uoadl:3035277 |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_relation |
uoadl:3035277 https://pergamos.lib.uoa.gr/uoa/dl/object/uoadl:3035277 |
_version_ |
1790604063511937024 |