严格对角占优M-矩阵的逆矩阵的无穷大范数的上界估计

Estimation on upper bounds for the infinity norms of inverses for strictly diagonally dominant M-matrices

引入一组新的记号,给出严格对角占优M-矩阵及其逆矩阵元素关系的不等式,得到了逆矩阵的无穷大范数的上界估计式。给出矩阵A最小特征值的下界,从理论上证明了新估计式改进了某些现有文献的结果,同时数值算例说明了新估计式更精确。

Firstly,some new notations are introduced in this paper,and some inequalities of element relation on strictly diagonally dominant M-matrix and its inverse matrix are given,the new upper bound of the infinite norm of the inverse matrix are obtained.In addition,the lower bound of the smallest eigenvalue of matrix A is presented.It is proved theoretically that the new upper bounds improve some existing results,and numerical examples show that the new estimation is more accurate.