非奇异M-矩阵最小特征值的估计序列

Estimated sequences for the minimum eigenvalue of nonsingular M-matrices

研究非奇异M-矩阵A的最小特征值τ(A)的估计问题。利用Gerschgorin圆盘定理和逆矩阵元素的上界,给出非负矩阵B与A的逆矩阵A-1的Hadamard积的谱半径ρ(B°A-1)的新的上界估计式,利用该估计式给出τ(A)的单调递增的收敛的下界序列。数值算例表明,所得结果比现有估计精确,且在某些情况下能达到真值。

Consider the estimate problem of the minimum eigenvalue of nonsingular M-matrices. Using Gerschgorin＇s theorem and the upper bounds of the elements of A-1,some new upper bounds for the spectral radius of the Hadamard product,ρ（ B°A-1）,of a nonnegative matrix B and the inverse of A are obtained. From which,some monotone increasing and convergent sequences of lower bounds of τ（ A） are given. The results of numerical examples show that the obtained estimations are more accurate than some existing results and could reach the true value in some cases.