弱链对角占优M-矩阵最小特征值的下界研究

The Lower Bounds of Minimum Eigenvalue of Weakly Chained Dominant M-matrix

利用迭代的方法,借助弱链对角占优M-矩阵A的逆矩阵A-1的非主对角元素现有的上界估计式,给出了A-1非主对角元素新的提高的上界估计式以及主对角元素新的上下界估计式。把得到的这些新估计式与该类矩阵的最小特征值经典的下界估计式结合,得到新的下界。新的界提高了现有结果,且这些估计式只与矩阵元素有关,使得计算更加容易。

By using the iterative method and the upper bound of non diagonal elements of the inverse matrix A-1 of the weak chain of diagonal dominant M-matrix A,the new upper bounds of non diagonal elements,and the upper and lower bounds of diagonal elements are derived.Together with the classical lower bound of minimum eigenvalue ofτ(A)for this matrix,the new improved bounds are obtained.The proof of the theorem and numerical examples are illustrated,the new bound improves the existing results,and these estimates are related with matrix elements and therefore calculation is easier.