弱链对角占优M-矩阵 ‖ A −1 ‖ ∞ 上界改进的估计式
Improved Estimation on Upper Bounds for ‖ A −1 ‖ ∞ of Weakly Chained Diagonally Dominant M-Matrices
DOI: 10.12677/aam.2025.149406, PDF,    科研立项经费支持
作者: 赵仁庆：楚雄师范学院数学与统计学院，云南 楚雄
关键词: 弱链对角占优矩阵；M-矩阵；无穷大范数；上界；Weakly Chained Diagonal Dominant Matrix； M-Matrix； Infinity Norms； Upper Bound
摘要: 本文研究弱链对角占优M-矩阵 A 的逆矩阵的无穷大范数上界估计问题，给出矩阵 A 及其逆矩阵元素关系的不等式，结合新不等式得到了 ‖ A −1 ‖ ∞ 的上界新估计式，理论分析和数值算例表明新估计式改进了某些现有结果。
Abstract: In this paper, the problem of estimating the bounds of the infinite norm of the inverse matrix of a weakly chained dominant M-matrix A is studied. The inequalities of element relation on matrix A and its inverse matrix are given, combined with the new inequality, new estimation upper bounds of ‖ A −1 ‖ ∞ are obtained. The theory analysis and numerical examples show that the new estimations improve some of the related results.
文章引用：赵仁庆. 弱链对角占优M-矩阵 ‖ A −1 ‖ ∞ 上界改进的估计式[J]. 应用数学进展, 2025, 14(9): 123-129. https://doi.org/10.12677/aam.2025.149406

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