严格α-对角占优M-矩阵A的||A-1||∞的上界估计
Upper Estimates of ||A-1||∞ for Strictly α-Diagonally Dominant M-Matrices
DOI: 10.12677/PM.2023.136167, PDF,    科研立项经费支持
作者: 罗雨薇, 莫宏敏*, 陈胜男：吉首大学数学与统计学院，湖南 吉首
关键词: 严格α-对角占优矩阵；M-矩阵；无穷范数；上界；Strict α-Diagonally Dominant Matrix； M-Matrices； Infinite Norm； Upper Bound
摘要: 利用严格α-对角占优M-矩阵的元素性质，特殊矩阵级数的收敛性，矩阵范数的性质，矩阵分裂技巧以及严格对角占优M-矩阵逆的无穷范数上界，得到了严格α-对角占优M-矩阵A的||A-1||∞一个新的上界估计式。数值例子说明新估计式是可行的、有效的。
Abstract: By using the properties of elements of strictly α-diagonally dominant M-matrices, the convergence of special matrix series, the properties of matrix norm, matrix splitting techniques, and the infinite norm upper bound for the inverse of strictly diagonally dominant M-matrices, a new upper bound estimation formula of ||A-1||∞ for strictly α-diagonally dominant M-matrices is obtained. Numerical examples show that the new estimation formula is feasible and effective.
文章引用：罗雨薇, 莫宏敏, 陈胜男. 严格α-对角占优M-矩阵A的||A-1||∞的上界估计[J]. 理论数学, 2023, 13(6): 1643-1651. https://doi.org/10.12677/PM.2023.136167

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