正则M-矩阵平方根的一类不动点迭代法
A Class of Fixed-Point Iteration Method for the Square Root of Regular M-Matrices
DOI: 10.12677/aam.2026.154176, PDF,    国家自然科学基金支持
作者: 马琳璐, 关晋瑞*：太原师范学院数学与统计学院，山西 晋中；邵荣侠：新疆财经大学统计与数据科学学院，新疆 乌鲁木齐
关键词: 正则M-矩阵；平方根；不动点迭代法；收敛性分析；收敛率；Regular M-Matrix； Square Root； Fixed-Point Iterative Method； Convergence Analysis； Convergence Rate
摘要: 矩阵平方根在数学的很多领域中都有广泛的应用。为了探讨M-矩阵平方根的数值算法，提出了一类不动点迭代法计算正则M-矩阵的平方根，并对其收敛性进行了分析。该方法的可行性已通过数值实验进行了验证，且在一定条件下优于现有的若干算法。
Abstract: The square root of matrix has a wide range of applications in many fields of mathematics. In order to explore the numerical algorithms for the square root of an M-matrix, a class of fixed-point iteration method for computing the square root of a regular M-matrix is proposed, and the convergence of these methods is analyzed. The feasibility of this method has been theoretically analyzed and verified through numerical experiments, and under certain conditions, it outperforms several existing algorithms.
文章引用：马琳璐, 关晋瑞, 邵荣侠. 正则M-矩阵平方根的一类不动点迭代法[J]. 应用数学进展, 2026, 15(4): 483-492. https://doi.org/10.12677/aam.2026.154176

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