Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1993-2006.doi: 10.1007/s42967-024-00432-8

• ORIGINAL PAPERS • 上一篇    

On Cyclic Block Coordinate Descent Method for Solving Large Inconsistent Linear Systems

Ran-Ran Li1, Hao Liu1,2   

  1. 1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu, China;
    2. Shenzhen Research Institute, Shenzhen, 518063, Guangdong, China
  • 收稿日期:2024-01-12 修回日期:2024-05-17 接受日期:2024-05-21 出版日期:2024-09-19 发布日期:2024-09-19
  • 通讯作者: Hao Liu,E-mail:hliu@nuaa.edu.cn E-mail:hliu@nuaa.edu.cn
  • 基金资助:
    This research was supported in part by the National Natural Science Foundation of China (No. 11401305 and No. 11571171) and Shenzhen Science and Technology Program, China (No. JCYJ20230807142002006).

On Cyclic Block Coordinate Descent Method for Solving Large Inconsistent Linear Systems

Ran-Ran Li1, Hao Liu1,2   

  1. 1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu, China;
    2. Shenzhen Research Institute, Shenzhen, 518063, Guangdong, China
  • Received:2024-01-12 Revised:2024-05-17 Accepted:2024-05-21 Online:2024-09-19 Published:2024-09-19
  • Contact: Hao Liu,E-mail:hliu@nuaa.edu.cn E-mail:hliu@nuaa.edu.cn
  • Supported by:
    This research was supported in part by the National Natural Science Foundation of China (No. 11401305 and No. 11571171) and Shenzhen Science and Technology Program, China (No. JCYJ20230807142002006).

摘要: For solving large inconsistent linear systems, we research a novel format to enhance the numerical stability and control the complexity of the model. Based on the idea of two subspace iterations, we propose the max-residual two subspace coordinate descent (M2CD) method. To accelerate the convergence rate, we further present the cyclic block coordinate descent (CBCD) method. The convergence properties of these methods are analyzed, and their effectiveness is illustrated by numerical examples.

关键词: Inconsistent linear systems, Least-squares problem, Coordinate descent (CD) method, Convergence property

Abstract: For solving large inconsistent linear systems, we research a novel format to enhance the numerical stability and control the complexity of the model. Based on the idea of two subspace iterations, we propose the max-residual two subspace coordinate descent (M2CD) method. To accelerate the convergence rate, we further present the cyclic block coordinate descent (CBCD) method. The convergence properties of these methods are analyzed, and their effectiveness is illustrated by numerical examples.

Key words: Inconsistent linear systems, Least-squares problem, Coordinate descent (CD) method, Convergence property