A^(-1)B的无穷大范数的上界估计

Estimaion of Upper Bounds of A^(-1) B for the Infinity Norms

Dashnic-Zusmanovich矩阵作为一类特殊的H-矩阵在数值代数中有着重要作用.设A为Dashnic-Zusmanovich矩阵,B为一般矩阵,给出||A^(-1)B||∞的新上界.特别的,当B为单位矩阵时,得到了 Dashnic-Zusmanovich矩阵的逆矩阵的无穷大范数上界和最小奇异值下界,这些估计式仅利用矩阵A的元素表示.理论分析和数值算例表明新估计式推广和改进了文献中的结果.

As a special class of H-matrices,Dashnic-Zusmanovich matrix plays an important role in the numerical algebra.let A be a Dashnic-Zusmanovich matrix and B be a general matrix,A new upper bound of ||A^(-1)B||∞ is given in this paper.Especially,when the B is a unit matrix,the upper bound of the infinite norm of the inverse matrix of the DashnicZusmanovich matrix and the lower bound of the minimum singular value are obtained,And these estimations are represented only by elements of matrix A.The theoretical analysis and numerical examples show that the new bounds generalizes and improves many known results.