In this paper, we propose an orthogonal block wise Kaczmarz (POBK) algorithm based on preprocessing techniques to solve large-scale sparse linear systems $Ax=f$. Firstly, the Reverse Cuthill McKee Algorithm (RCM) algorithm is used to preprocess the linear system, and then a new partitioning strategy is proposed to divide orthogonal blocks into one category, in order to accelerate the convergence rate of the Kaczmarz algorithm. The convergence of the POBK algorithm has been theoretically proven, and a theoretical analysis of its faster convergence is also provided. In addition, the experimental results confirm that this algorithm is far superior to GRBK, RBK(k), and GREBK(k) algorithms in both iteration steps (IT) and CPU time aspects.

翻译：本文提出了一种基于预处理技术的正交分块Kaczmarz（POBK）算法，用于求解大规模稀疏线性系统$Ax=f$。首先，采用逆向Cuthill-McKee算法（RCM）对线性系统进行预处理，随后提出一种新的分块策略，将正交块归为一类，以加速Kaczmarz算法的收敛速度。理论证明了POBK算法的收敛性，并对其更快的收敛速度进行了理论分析。此外，实验结果证实，该算法在迭代步数（IT）和CPU时间方面均远优于GRBK、RBK(k)和GREBK(k)算法。