非奇异M-矩阵及其逆矩阵Hadamard积最小特征值的新下界

New Lower Bound for the Minimum Eigenvalue of the Hadamard Product of Nonsingular M-matrix and Its Inverse

针对非奇异M-矩阵及其逆矩阵Hadamard积的最小特征值问题,首先,回顾了已有文献应用矩阵的特征值存在域定理和逆矩阵元素的估计式;其次,结合M-矩阵Hadamard积的相关性质特征及不等式的构造、放缩技巧,给出了非奇异M-矩阵与其逆矩阵是双随机矩阵的Hadamard积的最小特征值下界τ(A°A^-1)的一个仅与A矩阵的元素相关的估计式,推广了已有文献的结果;最后,用数值例子表明所给估计式的下界比已有结果得到的下界更精确.

For the problem of the minimum eigenvalue for the Hadamard product on nonsingular M-matrix and its Inverse,firstly,recalling the domain theorem of the eigenvalues for the matrix and the estimation formula for the elements of inverse matrix are used in the literature.Secondly,when A is nonsingular M-matrix and A^-1 are doubly stochastic,τ(A ° A^-1)is given by combining with the relative properties of the Hadamard product of M-matrix and the construction and reduction techniques of inequalities,which is only related to the elements of the matrix,and theoretical analysis proves that it improves the results of existing literature;Finally,numerical examples show that the new lower bound is more accurate than the existing lower bound.