Abstract：Let A and B be both nonsingular M-matrices, and A-1 be the inverse matrix of A. In order to get the new lower bounds of the minimum eigenvalue τ(B·A-1) of the Hadamard product of B and A-1, firstly, we give some sequences of the upper and lower bounds of the elements of A-1 are given using the elements of A.Then, using these sequences and Brauer theorem, some monotone increasing and convergent sequences of lower bounds of τ(B·A-1) are obtained. Numerical examples are provided to verify the theoretical results, which show that these sequences of the lower bounds are more accurate than some existing results and can reach the true value of the minimum eigenvalue.
赵建兴, 桑彩丽. 非奇异M-矩阵Hadamard积的最小特征值的新下界[J]. 浙江大学学报（理学版）, 2017, 44(5): 505-510,515.
ZHAO Jianxing, SANG Caili. New lower bounds for the minimum eigenvalue of the Hadamard product of nonsingular M-matrices. Journal of ZheJIang University(Science Edition), 2017, 44(5): 505-510,515.
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2017, Vol. 44 
