计算数学 ›› 2021, Vol. 43 ›› Issue (1): 118-132.DOI: 10.12286/jssx.j2020-0660

• 论文 • 上一篇    

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

丁戬, 殷俊锋   

  1. 同济大学 数学科学学院, 上海 200092
  • 收稿日期:2020-01-09 出版日期:2021-02-15 发布日期:2021-02-04
  • 基金资助:
    本研究受到国家自然科学基金（项目号：11971354）资助.
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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.

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.

THE RELAXATION TWO-SWEEP MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS

Ding Jian, Yin Junfeng   

  1. School of Mathematical Sciences, Tongji University, Shanghai 200092, China
  • Received:2020-01-09 Online:2021-02-15 Published:2021-02-04
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.
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
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.
Key words: Nonlinear complementarity problems, Matrix splitting, Two-sweep modulusbased iteration methods, Positive definite matrix, H+-matrix

MR(2010)主题分类: 

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季刊，创刊于1979年
主办：中国科学院数学与系统科学研究院
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