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线性互补问题的广义松弛两步模基矩阵分裂迭代法

彭小飞

彭小飞. 线性互补问题的广义松弛两步模基矩阵分裂迭代法[J]. 华南师范大学学报(自然科学版), 2019, 51(4): 93-99. doi: 10.6054/j.jscnun.2019071
引用本文: 彭小飞. 线性互补问题的广义松弛两步模基矩阵分裂迭代法[J]. 华南师范大学学报(自然科学版), 2019, 51(4): 93-99. doi: 10.6054/j.jscnun.2019071
PENG Xiaofei. A General Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems[J]. Journal of South China normal University (Natural Science Edition), 2019, 51(4): 93-99. doi: 10.6054/j.jscnun.2019071
Citation: PENG Xiaofei. A General Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems[J]. Journal of South China normal University (Natural Science Edition), 2019, 51(4): 93-99. doi: 10.6054/j.jscnun.2019071

线性互补问题的广义松弛两步模基矩阵分裂迭代法

doi: 10.6054/j.jscnun.2019071
基金项目: 

国家自然科学基金项目 11571124

国家自然科学基金项目 11801097

详细信息
    通讯作者:

    彭小飞, 副教授, Email:pxf6628@163.com

  • 中图分类号: O241.6

A General Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

  • 摘要: 将松弛策略引入到与线性互补问题等价的广义隐式定点迭代方程, 建立了求解线性互补问题的广义松弛两步模基矩阵分裂迭代法, 将已有的松弛两步模基矩阵分裂迭代法扩展到了更一般的情形; 当系数矩阵为H+-矩阵时, 利用H+-矩阵的特殊性质, 给出了新方法的收敛性分析.数值结果表明:依据迭代次数和CPU时间, 由新方法所导出的新的广义方法比已有的广义模基矩阵分裂迭代法和广义两步模基矩阵分裂迭代法更有效.
  • 表  1  广义方法计算例1和例2的拟最优参数(m=40)

    Table  1.   Quasi-optimal parameters of general methods for Exam-ple 1 and Example 2 (m=40)

    μ 拟最优参数 例1 例2
    0.5 (α*1, k*1) (2.2, 0.1) (1.7, 0.1)
    (α*2, k*2) (2.3, 0.4) (1.7, 0.3)
    (α*3, k*3) (2.1, 0.1) (1.5, 0.1)
    1.5 (α*1, k*1) (1.3, 1.8) (1.3, 1.2)
    (α*2, k*2) (1.4, 1.9) (1.9, 0.3)
    (α*3, k*3) (1.4, 1.9) (1.3, 1.2)
    2.5 (α*1, k*1) (1.2, 1.9) (1.2, 1.4)
    (α*2, k*2) (1.3, 1.8) (1.2, 1.4)
    (α*3, k*3) (1.2, 2.0) (1.2, 1.4)
    下载: 导出CSV

    表  2  广义方法计算例1和例2的数值结果

    Table  2.   Numerical results of general methods for Example 1 and Example 2

    μ m 方法 例1 例2
    IT tCPU RES IT tCPU RES
    0.5 40 GMSOR 65 0.029 8 9.9e-06 24 0.009 5 8.9e-06
    GTMSOR 58 0.021 9 9.0e-06 39 0.015 2 8.7e-06
    GNTMSOR 40 0.015 4 8.6e-06 25 0.009 9 6.4e-06
    80 GMSOR 66 0.103 7 9.1e-06 24 0.037 5 9.1e-06
    GTMSOR 60 0.094 6 9.1e-06 39 0.059 1 8.8e-06
    GNTMSOR 41 0.063 0 9.6e-06 25 0.041 9 9.5e-06
    120 GMSOR 66 0.237 2 9.7e-06 24 0.085 6 9.2e-06
    GTMSOR 61 0.215 3 9.3e-06 39 0.139 4 8.9e-06
    GNTMSOR 43 0.154 8 8.4e-06 27 0.098 9 4.2e-06
    1.5 40 GMSOR 30 0.011 9 9.4e-06 21 0.008 5 6.4e-06
    GTMSOR 43 0.016 3 8.9e-06 41 0.015 6 8.0e-06
    GNTMSOR 26 0.010 1 8.7e-06 19 0.007 3 7.6e-06
    80 GMSOR 32 0.049 1 7.4e-06 22 0.033 6 7.7e-06
    GTMSOR 46 0.070 6 9.9e-06 43 0.066 2 7.7e-06
    GNTMSOR 28 0.042 8 7.6e-06 20 0.030 6 7.4e-06
    120 GMSOR 33 0.122 0 6.9e-06 23 0.084 3 6.6e-06
    GTMSOR 48 0.171 9 9.3e-06 43 0.153 7 9.9e-06
    GNTMSOR 29 0.104 7 7.1e-06 21 0.077 2 5.6e-06
    2.5 40 GMSOR 21 0.007 6 9.5e-06 16 0.006 3 8.1e-06
    GTMSOR 30 0.011 8 8.6e-06 31 0.011 7 7.7e-06
    GNTMSOR 23 0.008 7 7.8e-06 16 0.006 1 8.0e-06
    80 GMSOR 22 0.034 1 8.1e-06 17 0.026 6 7.6e-06
    GTMSOR 31 0.048 8 7.7e-06 33 0.050 7 7.4e-06
    GNTMSOR 24 0.037 5 9.8e-06 17 0.026 1 6.2e-06
    120 GMSOR 23 0.083 6 5.6e-06 18 0.066 8 5.2e-06
    GTMSOR 31 0.112 6 9.5e-06 35 0.126 4 5.0e-06
    GNTMSOR 25 0.090 6 8.6e-06 17 0.062 9 8.9e-06
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-04-30
  • 刊出日期:  2019-08-25

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