| 求解广义绝对值方程的交替牛顿矩阵多分裂方法 |
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| 引用本文： | 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. |
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| 作者姓名： | 吴宇虹 马昌凤 |
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| 作者单位： | 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 |
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| 基金项目： | 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. |
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| 摘 要： | 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.
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| 关 键 词： | 广义绝对值方程 牛顿法 矩阵多分裂方法 |
| 收稿时间： | 2021-08-27 |
NEWTON-BASED ALTERNATE MATRIX MULTI-SPLITTING METHOD FOR GENERALIZED ABSOLUTE VALUE EQUATION |
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| 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. |
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| Authors: | Wu Yuhong Ma Changfeng |
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| Institution: | School of Mathematics and Statistics, FJKLMAA & Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou 350117, China |
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| Abstract: | 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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| Keywords: | generalized absolute value equation Newton method Matrix multi-splitting method |
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