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Keywords:
lower bound sequence; Hadamard product; $M$-matrix; doubly stochastic matrix; $S$-type eigenvalue inclusion set
lower bound sequence; Hadamard product; $M$-matrix; doubly stochastic matrix; $S$-type eigenvalue inclusion set
Summary:
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.
References:
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