A Note on the Inner-Outer Iterative Method for Solving the Linear Equation Ax = b

Author:

Zhang Li-Tao123ORCID,Zuo Xian-Yu4,Gu Tong-Xiang5,Wang Yan-Ping1,Zhang Yi-Fan1,Li Jian-Lei6,Li Sheng-Kun7

Affiliation:

1. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, Henan 450015, China

2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China

3. Henan Province Synergy Innovation Center of Aviation Economic Development, Zhengzhou, Henan 450015, China

4. Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China

5. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

6. College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China

7. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, China

Abstract

Recently, Tian et al. [Computers and Mathematics with Applications, 75(2018): 2710-2722] came up with the inner-outer iterative method to solve the linear equation Ax=b and studied the corresponding convergence of the method. In this paper, we improve the main results of the inner-outer method and get weaker convergence results. Moreover, the parameters can be adjusted suitably so that the convergence property of the method can be substantially improved.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Mathematics

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