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求解广义绝对值方程的交替牛顿矩阵多分裂方法

吴宇虹, 马昌凤   

  1. 福建师范大学 数学与统计学院, 福建省分析数学及应用重点实验室, 福建省应用数学中心, 福州 350117
  • 收稿日期:2021-08-27 出版日期:2022-07-14 发布日期:2022-08-03
  • 基金资助:
    国家重点研发计划项目(2019YFC0312003)和国家自然科学基金项目(11901098)资助.

吴宇虹, 马昌凤. 求解广义绝对值方程的交替牛顿矩阵多分裂方法[J]. 计算数学, 2022, 44(3): 422-432.

Wu Yuhong, Ma Changfeng. NEWTON-BASED ALTERNATE MATRIX MULTI-SPLITTING METHOD FOR GENERALIZED ABSOLUTE VALUE EQUATION[J]. Mathematica Numerica Sinica, 2022, 44(3): 422-432.

NEWTON-BASED ALTERNATE MATRIX MULTI-SPLITTING METHOD FOR GENERALIZED ABSOLUTE VALUE EQUATION

Wu Yuhong, Ma Changfeng   

  1. School of Mathematics and Statistics, FJKLMAA & Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou 350117, China
  • Received:2021-08-27 Online:2022-07-14 Published:2022-08-03
本文针对广义绝对值方程,提出了基于牛顿法的矩阵多分裂方法.并在该方法的基础上进一步改进,得到了基于牛顿法的交替矩阵多分裂方法.给出两种算法在一定条件下的全局收敛性,并分析当分裂为H分裂时,基于牛顿法的矩阵多分裂方法的收敛条件.通过数值实验验证了所提出的算法的可行性和有效性.
In this paper, a Newton-based matrix multi-splitting method is proposed for the generalized absolute value equation. Furthermore, a Newton-based alternate matrix multi-splitting method is obtained. The global convergence of the two algorithms under certain conditions is given, and the convergence condition of the Newton-based matrix multi-splitting method is analyzed when the splitting is H-splitting. The feasibility and effectiveness of the proposed algorithms are proved by numerical experiments.

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