双严格对角占优矩阵最小特征值的下界

The lower bound for the minimum eigenvalue of a doubly strictly diagonally dominant matrix

首先给出了双严格对角占优矩阵逆矩阵元素的界,其次利用这些界和矩阵特征值定位定理,得到了该矩阵最小特征值的下界.理论证明和数值算例都说明,新界提高了现有的结果.

This paper first gives the bounds of the elements of the inverse matrix for a doubly strictly diagonally dominant matrix. Then using these bounds and the eigenvalue theorem of the matrix, it gets the lower bound for the minimum eigenvalue of the matrix. The theoretical proof and numerical examples have proved that the new bound can improve the existing results.