ORIGINAL PAPERS

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

  • Yan-Xia Dai ,
  • Ren-Yi Yan ,
  • Ai-Li Yang
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  • 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 date: 2023-10-10

  Revised date: 2024-02-26

  Accepted date: 2024-03-22

  Online published: 2024-06-13

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].

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.

Cite this article

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 . DOI: 10.1007/s42967-024-00403-z

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