An innovative algorithm for estimating the minimum eigenvalue of M-matrices
Abstract For a general M-matrix, we construct a specialized matrix to derive monotonically increasing lower bounds and monotonically decreasing upper bounds for its minimum eigenvalue. These results generalize and significantly improve upon existing related findings. Furthermore, we rigorously prove...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03335-1 |
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| _version_ | 1849738327171792896 |
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| author | Qin Zhong Ling Li Gufang Mou |
| author_facet | Qin Zhong Ling Li Gufang Mou |
| author_sort | Qin Zhong |
| collection | DOAJ |
| description | Abstract For a general M-matrix, we construct a specialized matrix to derive monotonically increasing lower bounds and monotonically decreasing upper bounds for its minimum eigenvalue. These results generalize and significantly improve upon existing related findings. Furthermore, we rigorously prove the monotonicity and convergence properties of these bounds. Finally, for a non-defective M-matrix, we propose a smoothing algorithm to compute its minimum eigenvalue, and we validate the effectiveness of the algorithm through numerical examples. |
| format | Article |
| id | doaj-art-720fa5efb5d745d19a608b11685df3b7 |
| institution | DOAJ |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-720fa5efb5d745d19a608b11685df3b72025-08-20T03:06:39ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-07-012025111410.1186/s13660-025-03335-1An innovative algorithm for estimating the minimum eigenvalue of M-matricesQin Zhong0Ling Li1Gufang Mou2Department of Mathematics, Sichuan University Jinjiang CollegeSchool of Big Data and Artificial Intelligence, Chengdu Technological UniversityCollege of Applied Mathematics, Chengdu University of Information TechnologyAbstract For a general M-matrix, we construct a specialized matrix to derive monotonically increasing lower bounds and monotonically decreasing upper bounds for its minimum eigenvalue. These results generalize and significantly improve upon existing related findings. Furthermore, we rigorously prove the monotonicity and convergence properties of these bounds. Finally, for a non-defective M-matrix, we propose a smoothing algorithm to compute its minimum eigenvalue, and we validate the effectiveness of the algorithm through numerical examples.https://doi.org/10.1186/s13660-025-03335-1M-matrixMinimum eigenvalueUpper boundLower boundNon-defective matrix |
| spellingShingle | Qin Zhong Ling Li Gufang Mou An innovative algorithm for estimating the minimum eigenvalue of M-matrices Journal of Inequalities and Applications M-matrix Minimum eigenvalue Upper bound Lower bound Non-defective matrix |
| title | An innovative algorithm for estimating the minimum eigenvalue of M-matrices |
| title_full | An innovative algorithm for estimating the minimum eigenvalue of M-matrices |
| title_fullStr | An innovative algorithm for estimating the minimum eigenvalue of M-matrices |
| title_full_unstemmed | An innovative algorithm for estimating the minimum eigenvalue of M-matrices |
| title_short | An innovative algorithm for estimating the minimum eigenvalue of M-matrices |
| title_sort | innovative algorithm for estimating the minimum eigenvalue of m matrices |
| topic | M-matrix Minimum eigenvalue Upper bound Lower bound Non-defective matrix |
| url | https://doi.org/10.1186/s13660-025-03335-1 |
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