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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03335-1 |
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| Summary: | 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. |
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| ISSN: | 1029-242X |