非奇异M-矩阵Hadamard积的最小特征值的新下界

New lower bounds for the minimum eigenvalue of the Hadamard product of nonsingular M-matrices

针对非奇异M-矩阵B与非奇异M-矩阵A的逆矩阵A^(-1)的Hadamard积的最小特征值τ(B·A^(-1))的估计问题,首先利用矩阵A的元素给出A^(-1)各元素的上下界序列,然后利用这些序列和Brauer定理给出τ(B·A^(-1))单调递增收敛的下界序列.最后,通过数值算例验证理论结果,显示所得下界序列比现有结果精确,且能收敛到真值.

Let Aand Bbe both nonsingular M-matrices,and A^-1 be the inverse matrix of A.In order to get the new lower bounds of the minimum eigenvalueτ（B·A^-1）of the Hadamard product of Band A^-1,firstly,we give some sequences of the upper and lower bounds of the elements of A^-1are given using the elements of A.Then,using these sequences and Brauer theorem,some monotone increasing and convergent sequences of lower bounds ofτ（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.