1. Orthogonal Block Kaczmarz Algorithm Based on Preprocessing Technology
- Author
-
Liang, Yu-Fang and Li, Hou-Biao
- Subjects
Mathematics - Numerical Analysis ,65F10, 65F20, 65K05, 15A06 - Abstract
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., Comment: 25 pages, 12 figures, 3 tables
- Published
- 2024