非奇异M-矩阵最小特征值的下界序列

Sequences of Lower Bounds for Minimum Eigenvalue of Nonsingular M-Matrices

针对非奇异M-矩阵A的最小特征值τ(A)的估计问题,利用Brauer定理和逆矩阵元素的上界序列,给出了τ(A)的单调递增的收敛的下界序列.最后通过数值算例对理论结果进行验证,数值算例显示,所得下界序列比现有结果精确,且在某些情况下能达到真值.

For the lower bounds of the minimum eigenvalueτ（A）of nonsingular M-matrix A,some monotone increasing and convergent sequences of lower bounds ofτ（A）are obtained by using Brauer＇s theorem and the upper bounds of A^-1.Finally,numerical examples have been given to verify the theoretical results,showing that these sequences of lower bounds are more accurate than some existing results and could reach the true value of the minimum eigenvalue in some cases.