中文摘要：

针对逆矩阵的无穷大范数的上界估计问题,利用矩阵分裂方法和严格对角占优M-矩阵逆的无穷大范数的单调递减的上界序列,给出严格α2-对角占优M-矩阵A的‖A-1‖∞的单调递减的上界序列.最后通过数值算例对理论结果进行验证,数值算例显示所给方法是可行的,且优于某些已有结果.

英文摘要：

A monotone decreasing sequence of upper bounds for‖A-1‖∞ of a strictlyα2-diagonally dominant M-matrix Ais given with matrix splitting method and some existing upper bounds of the infinity norm of the inverse of strictly diagonally dominant M-matrices.Finally,numerical example is given to verify the theoretical results,and shows that the method in this paper is feasible and better than some existing results.