For solving large-scale consistent systems of linear equations by iterative methods, a fast block Kaczmarz method based on a greedy criterion of the row selections is proposed. The method is deterministic and needs not compute the pseudoinverses of submatrices or solve subsystems. It is proved that the method will converge linearly to the unique least-norm solutions of the linear systems. Numerical experiments are given to illustrate that the method is more efficient and yields a significant acceleration in convergence for the tested data.

中文翻译：

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求解大规模线性系统的快速确定性分块 Kaczmarz 方法

针对迭代法求解大规模一致线性方程组，提出了一种基于行选择贪婪准则的快速分块Kaczmarz方法。该方法是确定性的，不需要计算子矩阵的伪逆或求解子系统。证明该方法将线性收敛到线性系统的唯一最小范数解。给出了数值实验以说明该方法更有效并且对测试数据产生显着的收敛加速。