| 求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法 |
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| 引用本文： | 丁戬,殷俊锋.求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法[J].计算数学,2021,43(1):118-132. |
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| 作者姓名： | 丁戬 殷俊锋 |
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| 作者单位： | 同济大学数学科学学院,上海200092;同济大学数学科学学院,上海200092 |
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| 基金项目： | 本研究受到国家自然科学基金 |
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| 摘 要： | 本文构造了求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法. 理论分析建立了新方法在系数矩阵为正定矩阵或H+矩阵时的收敛性质．数值实验结果表明新方法是行之有效的, 并且在最优参数下松弛two-sweep模系矩阵分裂迭代法在迭代步数和时间上均优于传统的模系矩阵分裂迭代法和two-sweep模系矩阵分裂迭代法.
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| 关 键 词： | 非线性互补问题 矩阵分裂 松弛two-sweep模系迭代法 正定矩阵 H+阵 |
| 收稿时间： | 2020-01-09 |
THE RELAXATION TWO-SWEEP MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS |
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| Ding Jian,Yin Junfeng.THE RELAXATION TWO-SWEEP MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS[J].Mathematica Numerica Sinica,2021,43(1):118-132. |
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| Authors: | Ding Jian Yin Junfeng |
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| Affiliation: | School of Mathematical Sciences, Tongji University, Shanghai 200092, China |
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| Abstract: | To solve a class of nonlinear complementarity problems,the relaxation modulus-based matrix splitting iteration methods are presented and analyzed.Convergence theory is established when the system matrix is a positive definite matrix or an H+-matrix.Numerical experiments show that the proposed methods are efficient and better than the modulusbased matrix splitting iteration methods and the two-sweep modulus-based matrix splitting iteration methods in aspects of iteration steps and CPU time. |
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| Keywords: | Nonlinear complementarity problems Matrix splitting Two-sweep modulusbased iteration methods Positive definite matrix H+-matrix |
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