井冈山大学学报（自然科学版）2025，Vol.46Issue(5)：12-18,7.DOI:10.3969/j.issn.1674-8085.2025.05.002
松弛贪婪随机块Kaczmarz方法求解四元数线性系统
RELAXED GREEDY RANDOMIZED BLOCK KACZMARZ METHOD FOR SOLVING QUATERNION LINEAR SYSTEMS
摘要
Abstract
The randomized block Kaczmarz method is an iterative method for solving large-scale linear systems.At each iteration,the algorithm orthogonally projects the current iteration point onto the solution space of the constrained subset.This study proposes a relaxed greedy randomized block Kaczmarz(QRGRBK)method for the quaternion linear systems and proves its convergence.Through numerical experiments,the feasibility and effectiveness of the QRGRBK method have been successfully validated.Furthermore,the application of the QRGRBK method in image restoration has been demonstrated,which provides substantial evidence for its practical utility and computational efficiency in real-world scenarios.关键词
四元数线性系统/随机块Kaczmarz方法/松弛贪婪选择策略/收敛性分析Key words
quaternion linear systems/randomized block Kaczmarz method/relaxed greedy selection strategy/convergence analysis分类
数理科学引用本文复制引用
郑月桂,黄宝华..松弛贪婪随机块Kaczmarz方法求解四元数线性系统[J].井冈山大学学报（自然科学版）,2025,46(5):12-18,7.基金项目
国家自然科学基金青年项目(12001211) （12001211）
