The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices

The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, 2005) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that und...

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Detalles Bibliográficos
Autores principales: Zhang, Cheng-yi, Wang, Weiwei, Luo, Shuanghua, Zhao, Jianxing
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5382214/
https://www.ncbi.nlm.nih.gov/pubmed/28435205
http://dx.doi.org/10.1186/s13660-017-1340-0
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author Zhang, Cheng-yi
Wang, Weiwei
Luo, Shuanghua
Zhao, Jianxing
author_facet Zhang, Cheng-yi
Wang, Weiwei
Luo, Shuanghua
Zhao, Jianxing
author_sort Zhang, Cheng-yi
collection PubMed
description The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, 2005) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions the separation of the Schur complement of a nonstrictly diagonally dominant matrix is greater than that of the original grand matrix. As an application, the eigenvalue distribution of the Schur complement is discussed for nonstrictly diagonally dominant matrices to derive some significant conclusions. Finally, some examples are provided to show the effectiveness of theoretical results.
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spelling pubmed-53822142017-04-20 The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices Zhang, Cheng-yi Wang, Weiwei Luo, Shuanghua Zhao, Jianxing J Inequal Appl Research The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, 2005) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions the separation of the Schur complement of a nonstrictly diagonally dominant matrix is greater than that of the original grand matrix. As an application, the eigenvalue distribution of the Schur complement is discussed for nonstrictly diagonally dominant matrices to derive some significant conclusions. Finally, some examples are provided to show the effectiveness of theoretical results. Springer International Publishing 2017-04-05 2017 /pmc/articles/PMC5382214/ /pubmed/28435205 http://dx.doi.org/10.1186/s13660-017-1340-0 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhang, Cheng-yi
Wang, Weiwei
Luo, Shuanghua
Zhao, Jianxing
The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
title The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
title_full The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
title_fullStr The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
title_full_unstemmed The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
title_short The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
title_sort disc separation and the eigenvalue distribution of the schur complement of nonstrictly diagonally dominant matrices
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5382214/
https://www.ncbi.nlm.nih.gov/pubmed/28435205
http://dx.doi.org/10.1186/s13660-017-1340-0
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