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<p>For a general <i>M</i>-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 <i>M</i>-matrix, we propose a smoothing algorithm to compute its minimum eigenvalue, and we validate the effectiveness of the algorithm through numerical examples.</p>

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An innovative algorithm for estimating the minimum eigenvalue of M-matrices

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月7日

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  • Qin Zhong,
  • Ling Li,
  • Gufang Mou

摘要

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.