The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices
Abstract 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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1340-0 |
| _version_ | 1818574549926543360 |
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| author | Cheng-yi Zhang Weiwei Wang Shuanghua Luo Jianxing Zhao |
| author_facet | Cheng-yi Zhang Weiwei Wang Shuanghua Luo Jianxing Zhao |
| author_sort | Cheng-yi Zhang |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-15T00:28:02Z |
| format | Article |
| id | doaj.art-ae61ae11a5a04f72a7a39e8232cd24d2 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-15T00:28:02Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ae61ae11a5a04f72a7a39e8232cd24d22022-12-21T22:42:07ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-04-012017111210.1186/s13660-017-1340-0The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matricesCheng-yi Zhang0Weiwei Wang1Shuanghua Luo2Jianxing Zhao3School of Science, Xi’an Polytechnic UniversitySchool of Science, Xi’an Polytechnic UniversitySchool of Science, Xi’an Polytechnic UniversityCollege of Science, Guizhou Minzu UniversityAbstract 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.http://link.springer.com/article/10.1186/s13660-017-1340-0Geršgorin disc separationSchur complementnonstrictly diagonally dominant matriceseigenvalue distribution |
| spellingShingle | Cheng-yi Zhang Weiwei Wang Shuanghua Luo Jianxing Zhao The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices Journal of Inequalities and Applications Geršgorin disc separation Schur complement nonstrictly diagonally dominant matrices eigenvalue distribution |
| 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 | Geršgorin disc separation Schur complement nonstrictly diagonally dominant matrices eigenvalue distribution |
| url | http://link.springer.com/article/10.1186/s13660-017-1340-0 |
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