摘要
本文基于求解线性方程组的贪婪随机Kaczmarz算法和贪婪几何概率随机Kaczmarz算法的思想,提出求解矩阵方程的新型贪婪随机算法.而后,利用重要不等式探讨贪婪几何概率随机Kaczmarz算法的收敛性.最后,通过数值实验验证算法的可行性和有效性.数值结果表明:对于大规模矩阵方程,贪婪几何概率随机Kaczmarz算法优于贪婪随机Kaczmarz算法.
In this paper,firstly,inspired by the ideas of two algorithms:the greedy randomized Kaczmarz algorithm and the geometric probability randomized Kaczmarz algorithm for solving linear equations,two novel greedy randomized algorithms for solving matrix equations are proposed.Then,the convergence of these two methods in matrix equations is proved based on important inequalities.Finally,the numerical experiments are implemented to verify the effectiveness of the proposed methods.The numerical results show that the geometric probability randomized Kaczmarz algorithm outperforms the greedy randomized Kaczmarz algorithm for large-scale systems.
作者
念辰俣
鲍文娣
邓帅豪
刘帅东
王冬锐
Nian Chenyu;Bao Wendi;Deng Shuaihao;Liu Shuaidong;Wang Dongrui(School of Science,China University of Petroleum,Qingdao 266580,China)
出处
《数值计算与计算机应用》
2025年第3期189-202,共14页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(42176011,42374156)
中央高校基本科研业务费专项资金(24CX03001A)
大学生创新创业训练计划项目(202411008CX)
中国石油大学教改项目“基于OBE理念的《矩阵计算》课程思政教学改革与研究”(YJG2023050)资助。
关键词
贪婪算法
几何概率随机Kaczmarz算法
迭代法
收敛性
Greedy method
Geometric probability randomized method
Kaczmarz method
Iterative method
Convergence
