非奇异 M 矩阵的 Hadamard 积的最小特征值的下界序列
Sequences of Lower Bounds for Minimum Eigenvalue of Hadamard Product of Nonsingular M-Matrices
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摘要: 研究非奇异 M 矩阵A 与其逆A -1的 Hadamrad 积的最小特征值τ(A。A -1)的估计问题。首先利用矩阵 A 的元素给出A -1各元素的上界序列。接着利用这些上界序列和 Gerschgorin 定理、Brauer 定理分别给出τ(A。A -1)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 eigenvalueτ(A.A -1 )of the Hadamard product of anonsin-gular M-matrix A and its inverse,first of all,some sequences of upper bounds of the elements of A -1 are-given with the elements of A.And then several monotone increasing and convergent sequences of lower bounds ofτ(A.A -1 )are obtained with these bounds of A -1 ,Gerschgorin’s theorem and Brauer’s theorem. Finally,numerical examples have been given to verify the theoretical results,and show that these se-quences 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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