M-矩阵Fan积最小特征值的下界

Lower Bounds on the Minimum Eigenvalue of the Fan Product of M-matrices

关于非奇M-矩阵A与B的Fan积A★B,利用Gerschgorin圆盘定理和Brauer定理,给出A★B的最小特征值下界的新估计式。新估计式只与矩阵的元素有关。数值算例表明新估计式改进了现有的结果,易于计算。

If A and B are nonsingular M-matrices, some new lower bounds for the minimum eigenvalue of A★B are given by using Gerschgorin theorem and Brauer theorem. The example indicates that these bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depended on the entries of matrices A and B.