非奇异M-矩阵的Hadamard积的最小特征值的下界

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A^(-1)的Hadamrad积的最小特征值τ(BoA^(-1))的估计问题,给出A^(-1)各元素的上下界序列,利用这些序列和Gerschgorin圆盘定理,构造出τ(BoA^(-1))的单调递增的下界序列,并证明这些下界序列是收敛的,且比某些现有结果精确。数值算例表明,所得下界序列在某些情况下能收敛到真值。

Let A and B benonsingular M-matrices. For the lower bounds of the minimum eigenvalue τ（B . A - 1 ） of the Hadamard product of B and the inverse A-1 of A, some sequences of the upper and lower bounds of the elements of A-1 are given, and several monotone increasing sequences of lower bounds of τ（B . A-1） are obtained by using these sequences and Gerschgorin＇ s theorem. It is proved that these sequences of the lower bounds are convergent and more accurate than some existing results. Numerical examples are given to show that these sequences of the lower bounds could reach the true value of the minimum eigenvalue in some cases.