Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

doi:10.1007/s42967-024-00403-z

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1815-1825.doi: 10.1007/s42967-024-00403-z

• ORIGINAL PAPERS • 上一篇

Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

Yan-Xia Dai¹, Ren-Yi Yan², Ai-Li Yang¹

1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, Hainan, China;
2. School of Economics and Management, Hainan Normal University, Haikou, 571158, Hainan, China

收稿日期:2023-10-10 修回日期:2024-02-26 接受日期:2024-03-22 出版日期:2024-06-13 发布日期:2024-06-13
通讯作者: Ren-Yi Yan,E-mail:920188@hainnu.edu.cn;Ai-Li Yang,E-mail:yangaili@hainnu.edu.cn E-mail:920188@hainnu.edu.cn;yangaili@hainnu.edu.cn
基金资助:
This work is supported by the National Natural Science Foundation of China [Grant no. 12161030] and the Natural Science Foundation of Hainan Province China [Grant nos. 523MS039 and 121MS030].

Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

Yan-Xia Dai¹, Ren-Yi Yan², Ai-Li Yang¹

1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, Hainan, China;
2. School of Economics and Management, Hainan Normal University, Haikou, 571158, Hainan, China

Received:2023-10-10 Revised:2024-02-26 Accepted:2024-03-22 Online:2024-06-13 Published:2024-06-13
Contact: Ren-Yi Yan,E-mail:920188@hainnu.edu.cn;Ai-Li Yang,E-mail:yangaili@hainnu.edu.cn E-mail:920188@hainnu.edu.cn;yangaili@hainnu.edu.cn
Supported by:
This work is supported by the National Natural Science Foundation of China [Grant no. 12161030] and the Natural Science Foundation of Hainan Province China [Grant nos. 523MS039 and 121MS030].

摘要/Abstract

摘要： In this work, by applying the minimum residual technique to the block-diagonal and anti-block-diagonal splitting (BAS) iteration scheme, an iteration method named minimum residual BAS (MRBAS) is proposed to solve a two-by-two block system of nonlinear equations arising from the reformulation of the system of absolute value equations (AVEs). The theoretical analysis shows that the MRBAS iteration method is convergent under suitable conditions. Numerical results demonstrate the feasibility and the effectiveness of the MRBAS iteration method.

关键词: Absolute value equations (AVEs), Block-diagonal and anti-block-diagonal splitting (BAS), Minimum residual, Minimum residual BAS (MRBAS) iteration, Convergence analysis

Abstract: In this work, by applying the minimum residual technique to the block-diagonal and anti-block-diagonal splitting (BAS) iteration scheme, an iteration method named minimum residual BAS (MRBAS) is proposed to solve a two-by-two block system of nonlinear equations arising from the reformulation of the system of absolute value equations (AVEs). The theoretical analysis shows that the MRBAS iteration method is convergent under suitable conditions. Numerical results demonstrate the feasibility and the effectiveness of the MRBAS iteration method.

Key words: Absolute value equations (AVEs), Block-diagonal and anti-block-diagonal splitting (BAS), Minimum residual, Minimum residual BAS (MRBAS) iteration, Convergence analysis

Yan-Xia Dai, Ren-Yi Yan, Ai-Li Yang. Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1815-1825.

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Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

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