哈尔滨商业大学学报（自然科学版）2026，Vol.42Issue(1)：122-128,7.
不相容线性方程组的新型随机增广Kaczmarz方法
New randomized augmented Kaczmarz method for solving linear systems
摘要
Abstract
The greedy randomized augmented Kaczmarz(GRAK)method and its accelerated variant(AGRAK)method were effective iterative approaches for solving inconsistent linear systems transformed into consistent augmented linear systems.However,they still suffered from relatively high computational costs when handling large-scale problems.To improve the computational efficiency of the AGRAK method,a novel randomized augmented Kaczmarz method based on a maximum-distance row selection strategy,termed NRAK,was proposed.By optimizing the row selection mechanism at the current iterate,the proposed method accelerated the convergence of the method.Theoretical analysis showed that the proposed method converged exponentially in the mean square to the least squares solution,and under reasonable assumptions,the NRAK method achieved superior convergence rates compared to the AGRAK method.Numerical experiments further demonstrated that,compared with state-of-the-art methods,the NRAK method required fewer iterations and less computational time,which indicated that the NRAK method based on the maximum-distance row selection strategy effectively improved the computational efficiency for solving large-scale inconsistent linear systems.关键词
不相容线性方程组/增广线性系统/随机Kaczmarz方法/贪婪随机增广Kacz-marz方法/最大距离采样/收敛性Key words
inconsistent linear systems/augmented linear system/randomized Kaczmarz method/greedy randomized augmented Kaczmarz method/maximal-distance sampling/convergence property分类
数理科学引用本文复制引用
吕玉鑫,张建华..不相容线性方程组的新型随机增广Kaczmarz方法[J].哈尔滨商业大学学报（自然科学版）,2026,42(1):122-128,7.基金项目
国家自然科学基金(12061009) （12061009）
江西省自然科学基金面上项目(2020BAB201002) （2020BAB201002）
