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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (1): 45- 58.

• • 上一篇    下一篇

广义绝对值方程组的局部预条件类SOR方法

张珍珠1,  李朝迁2   

  1. 1. 汉江师范学院数学与计算机科学学院，十堰 442000
    2. 云南大学数学与统计学院，昆明 650504
  • 收稿日期:2022-07-24 接受日期:2023-03-29 出版日期:2025-02-15 发布日期:2025-04-15
  • 通讯作者: 李朝迁 E-mail: lichaoqian@ynu.edu.cn
  • 基金资助:
    国家自然科学基金(12061087).

A Local Preconditioned SOR-like Method for Generalized Absolute Value Equations

ZHANG Zhenzhu1,  LI Chaoqian2   

  1. 1. School of Mathematics and Computer Science, Hanjiang Normal University, Shiyan 442000
    2. School of Mathematics and Statistics, Yunnan University, Kunming 650504
  • Received:2022-07-24 Accepted:2023-03-29 Online:2025-02-15 Published:2025-04-15
  • Contact: C. Li. E-mail address: lichaoqian@ynu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (12061087).

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摘要：

广义绝对值方程组在经济、工程等领域有着重要作用，其求解已成为计算数学和优化方向的重要问题之一。基于广义绝对值方程组的等价形式及预条件技术，对求解广义绝对值方程组的高效算法进行了研究，提出了局部预条件类SOR迭代法，讨论了该方法的收敛性，并通过数值算例说明了该方法在某些情况下优于已有方法。

关键词: 广义绝对值方程组, 预条件, SOR迭代法, 类SOR法

Abstract:

Generalized absolute value equations play an important role in fields such as Economics and Engineering, and solving it has become one of the important problems in computational mathematics and optimization. Based on their equivalent forms and preconditioning techniques, we have conducted research on efficient algorithms for solving generalized absolute value equations, a local preconditioned SOR-like method is proposed. The convergence of this method is discussed. Numerical examples are also given to demonstrate that it outperforms some existing methods in some cases.

Key words: generalized absolute value equations, precondition, SOR iterative method, SOR-like method

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