非奇异M-矩阵最小特征值的下界估计

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

利用Brauer定理和逆矩阵元素的上界序列,给出非奇异M-矩阵A的逆矩阵A-1及非负矩阵B的Hadamard积的谱半径ρ(BA-1)的单调不增的上界序列,并利用该上界序列给出A的最小特征值τ(A)的单调不减的下界序列,通过数值算例验证了所得结果.数值结果表明,所得估计比某些已有结果更精确.

Using Brauer＇s theorem and sequences of upper bounds of the elements of inverse matrices, the author gave a monotone non-increasing sequences of upper bounds of the spectral radius p（B o A-1 ） for the Hadamard product of the inverse matrix A 1 of a nonsingular M-matrix A and a nonnegative matrix B and gave some monotone non-decreasing sequences of lower bounds for the minimum eigenvalue r（A） of A by using this sequences of upper bounds. The obtained results were verified by several numerical examples. Numerical results show that these obtained estimates are more accurate than some existing results.