非奇异M-矩阵特殊积最小特征值下界的新估计

Some New Lower Bounds on the Minimum Eigenvalue of Special Product of Nonsingular M-matrices

根据非奇异M-矩阵的性质和矩阵的特征值包含域定理,结合两个M-矩阵Hadamard积的特征,分别给出q(B°A-1)和q(A°A-1)下界的一个新估计式。对A-1是双随机矩阵时B与A-1的Hadamard积最小特征值下界的估计式进行改进,理论证明这些估计式改进了现有的结果,且这些估计式仅用到矩阵A和B的元素,计算更简捷。通过数值算例表明新估计式的优越性和有效性,估计结果更接近于真实值。

According to the properties of nonsingular M-matrices and the eigenvalue inclusion set,combined with the characteristics of the product of two M-matrices.some new estimation formulas on lower bounds of q(B°A-1)and q(A°A-1)are given.When A-1 is a doubly stochastic matrix,a new lower bound of the minimum eigenvalues of Hadamard product B and A-1 is derived.It is proved that these new bounds have improved the existing results,only applying to the elements of matrix A and B,with easy computation.The experimental date shows that these new inequalities are superior and more valid,and the estimated result is closer to the true value.