Abstract
In this paper, we propose a lower bound sequence for \(\tau \left( A \circ {A^{ - 1}}\right) \), the minimum eigenvalue of Hadamard product of an M-matrix and its inverse by constructing a vector x and a constant k such that \(A \circ {A^{ - 1}}x\ge kx\). We prove the convergence of the lower bound sequence, which is an improvement on some of the existing results. By introducing a parameter and modifying constantly x and k, a more precise lower bound sequence is obtained. An example is given to show that the truth value of the minimum eigenvalue can be obtained by applying the new theorem to some kind of cyclic matrix. And several numerical experiments are given to demonstrate that the new bounds are sharper than some existing ones in most cases.
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The authors would like to express their sincere thanks to the three unknown referees for their very constructive criticism. To all who contributed to the improvement of the quality of the presentation of this work the authors are most indebted.
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Communicated by Fatemeh Panjeh Ali Beik.
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The work was supported by the National Natural Science Foundation of China (11971413)
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Zeng, W., Liu, J. Lower Bound Estimation of the Minimum Eigenvalue of Hadamard Product of an M-Matrix and its Inverse. Bull. Iran. Math. Soc. 48, 1075–1091 (2022). https://doi.org/10.1007/s41980-021-00563-1
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DOI: https://doi.org/10.1007/s41980-021-00563-1