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
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摘要: 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。Abstract: For the lower bounds of the minimum eigenvalue τ(A) of nonsingular M-matrix A ,some mono-tone increasing and convergent sequences of lower bounds of τ(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 re-sults ,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 .
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