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Some Lower Bounds with a Parameter for the Minimum Eigenvalue of Hadamard Product of M-Matrices and Inverse M-Matrices

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Abstract

In this paper, we present some lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and inverse M-matrix, by virtue of some eigenvalue inclusion sets with parameter \(\alpha \) and inequality scaling techniques. And we analyze relationships between the sizes of the obtained lower bounds. A series of numerical examples are given to demonstrate that our results can be more accurate than the existing results by selecting an appropriate parameter \(\alpha \).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Wenlong Zeng, Jianzhou Liu & Juan Wang

  2. Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan, People’s Republic of China

    Wenlong Zeng, Jianzhou Liu & Juan Wang

Authors
  1. Wenlong Zeng
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  2. Jianzhou Liu
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  3. Juan Wang
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Correspondence to Jianzhou Liu.

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Communicated by Fatemeh Panjeh Ali Beik.

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The work is supported partly by National Natural Science Foundation of China (Grant No. 11971413) and Postgraduate Scientific Research Innovation Project of Hunan Province (Grant No. CX20210513).

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Zeng, W., Liu, J. & Wang, J. Some Lower Bounds with a Parameter for the Minimum Eigenvalue of Hadamard Product of M-Matrices and Inverse M-Matrices. Bull. Iran. Math. Soc. 48, 3947–3970 (2022). https://doi.org/10.1007/s41980-022-00728-6

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  • DOI: https://doi.org/10.1007/s41980-022-00728-6

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