We propose a randomized block extended Kaczmarz method with hybrid partitioning techniques for solving large inconsistent linear systems. It employs the -means clustering to partition the columns of the coefficient matrix while applying the uniform sampling to derive the row partition of the coefficient matrix. It is proved that the proposed algorithm converges to the unique least-squares least-norm solution in expectation. Numerical examples validate that the new algorithm is competitive when compared with other randomized extended Kaczmarz-type methods.

中文翻译：

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用于求解大型不一致线性系统的混合分区随机块扩展 Kaczmarz 方法

我们提出了一种采用混合分区技术的随机块扩展 Kaczmarz 方法，用于解决大型不一致线性系统。它采用均值聚类来划分系数矩阵的列，同时应用均匀采样来导出系数矩阵的行划分。证明了该算法按预期收敛到唯一的最小二乘最小范数解。数值例子验证了新算法与其他随机扩展 Kaczmarz 型方法相比具有竞争力。