  In this paper, a new simple and fast orthogonal block Kaczmarz (POBK)
algorithm based on preprocessing techniques is proposed to solve large-scale
sparse linear systems Ax = f. Firstly, the sparse Reverse Cuthill-McKee
Algorithm (RCM) is used to preprocess the linear system, and then a new
partitioning strategy is proposed to divide the mutually orthogonal blocks into
one category, which greatly reduces computational complexity. In addition, we
provide a theoretical proof of the convergence of the POBK algorithm and
analyze its faster convergence. Finally, numerical simulations demonstrate that
our method outperforms the latest Kaczmarz methods such as GRBK, RBK(k),
GREBK(k), and aRBK in terms of CPU time.
