Geodesic
A lower bound sequence for the minimum eigenvalue of Hadamard product of an $M$-matrix and its inverse
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 663-679
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We propose a lower bound sequence for the minimum eigenvalue of Hadamard product of an $M$-matrix and its inverse, in terms of an $S$-type eigenvalues inclusion set and inequality scaling techniques. In addition, it is proved that the lower bound sequence converges. Several numerical experiments are given to demonstrate that the lower bound sequence is sharper than some existing ones in most cases.
We propose a lower bound sequence for the minimum eigenvalue of Hadamard product of an $M$-matrix and its inverse, in terms of an $S$-type eigenvalues inclusion set and inequality scaling techniques. In addition, it is proved that the lower bound sequence converges. Several numerical experiments are given to demonstrate that the lower bound sequence is sharper than some existing ones in most cases.
DOI : 10.21136/CMJ.2021.0092-21
Classification : 15A18, 15A42
Keywords: lower bound sequence; Hadamard product; $M$-matrix; doubly stochastic matrix; $S$-type eigenvalue inclusion set 
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Zeng, Wenlong; Liu, Jianzhou. A lower bound sequence for the minimum eigenvalue of Hadamard product of an $M$-matrix and its inverse. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 663-679. doi: 10.21136/CMJ.2021.0092-21

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