Czechoslovak Mathematical Journal, Vol. 72, No. 3, pp. 663-679, 2022
A lower bound sequence for the minimum eigenvalue of Hadamard product of an $M$-matrix and its inverse
Wenlong Zeng, Jianzhou Liu
Received March 13, 2021. Published online December 20, 2021.
Abstract: 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.
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Affiliations: Wenlong Zeng, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P. R. China, e-mail: xtuzwl@163.com; Jianzhou Liu (corresponding author), School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P. R. China, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China, e-mail: liujz@xtu.edu.cn
