删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

一类H矩阵线性互补问题的预处理二步模基矩阵分裂迭代方法

本站小编 Free考研考试/2021-12-27

郑华, 罗静
韶关学院, 数学与统计学院, 韶关 512005
收稿日期:2016-05-12出版日期:2018-03-15发布日期:2018-02-03
通讯作者:罗静,guluojing@163.com.

基金资助:国家自然科学基金(11601340),广东省高性能计算学会开放基金项目(2017060108),广东省数据科学工程技术研究中心开放基金项目(2016KF11),韶关市科技计划项目(韶科[2016]44/15),韶关学院科研项目(S201501021).


A PRECONDITIONED TWO-STEPS MODULUS-BASEDMATRIX SPLITTING ITERATION METHOD FORSOLVING LINEAR COMPLEMENTARITYPROBLEMS OF H-MATRICES

Zheng Hua, Luo Jing
School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China
Received:2016-05-12Online:2018-03-15Published:2018-02-03







摘要



编辑推荐
-->


本文我们利用预处理技术推广了求解线性互补问题的二步模基矩阵分裂迭代法,并针对H-矩阵类给出了新方法的收敛性分析,得到的理论结果推广了已有的一些方法.
MR(2010)主题分类:
65F08
65F10

分享此文:
H矩阵线性互补问题的预处理二步模基矩阵分裂迭代方法”的文章,特向您推荐。请打开下面的网址:http://www.computmath.com/jssx/CN/abstract/abstract197.shtml' name="neirong">H矩阵线性互补问题的预处理二步模基矩阵分裂迭代方法'>

()

[1] Cottle R W, Pang J S and Stone R E. The Linear Complementarity Problem[M]. SIAM Publisher, Philadelphia, 2009.

[2] Ferris M C and Pang J S. Engineering and economic applications of complementarity problems[J]. SIAM Reviews, 1997, 39:669-713.

[3] Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numer. Linear Algebra Appl., 2010, 17:917-933.

[4] Bai Z Z and Zhang L L. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems[J]. Numer. Linear Algebra Appl., 2013, 20:425-439.

[5] Bai Z Z and Zhang L L. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems[J]. Numer. Algorithms, 2013, 62:59-77.

[6] Dong J L and Jiang M Q. A modified modulus method for symmetric positive-definite linear complementarity problems[J]. Numer. Linear Algebra Appl., 2009, 16:129-143.

[7] Hadjidimos A and Tzoumas M. Nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem[J]. Linear Algebra Appl., 2009, 431:197-210.

[8] van Bokhoven W M G. Piecewise-linear Modelling and Analysis[M]. Proefschrift, Eindhoven, 1981.

[9] Li W. A general modulus-based matrix splitting method for linear complementarity problems of H-matrices[J]. Appl. Math. Lett., 2013, 26:1159-1164.

[10] Zhang L L and Ren Z R. Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Appl. Math. Lett., 2013, 26:638-642.

[11] Zhang L L. Two-step modulus based matrix splitting iteration for linear complementarity problems[J]. Numer. Algorithms, 2011, 57:83-99.

[12] Zhang L L. Two-stage multisplitting iteration methods using modulus-based matrix splitting as inner iteration for linear complementarity problems. Journal of Optimization Theory and Applications[J]. 2014, 160:189-203.

[13] Zheng N, Yin J F. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numer. Algorithms, 2013, 64:245-262.

[14] Liu S M, Zheng H, Li W. A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems[J]. CALCOLO, 2016, 53:189-199.

[15] Zheng H, Li W, Vong S. A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems[J]. Numer. Algorithms, 2017, 74:137-152.

[16] Li W and Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices[J]. Linear and Multilinear Algebra, 2016, 64:1390-1403.

[17] Berman A and Plemmons R J. Nonnegative Matrices in the Mathematical Sciences[M]. SIAM Publisher, Philadelphia, 1994.

[18] Bai Z Z. On the convergence of the multisplitting methods for the linear complementarity problem[J]. SIAM J. Matrix Anal. Appl., 1999, 21:67-78.

[19] Frommer A and Mayer G. Convergence of relaxed parallel multisplitting methods[J]. Linear Algebra Appl., 1989, 119:141-152.

[20] Hu J G, Estimates of||B-1 A|| and their applications[J]. Mathematica Numerica Sinica, 1982, 4:272-282.

[1]吴敏华, 李郴良. 求解带Toeplitz矩阵的线性互补问题的一类预处理模系矩阵分裂迭代法[J]. 计算数学, 2020, 42(2): 223-236.
[2]曹阳, 陈莹婷. 正则化HSS预处理鞍点矩阵的特征值估计[J]. 计算数学, 2020, 42(1): 51-62.
[3]王丽, 罗玉花, 王广彬. 求解加权线性最小二乘问题的一类预处理GAOR方法[J]. 计算数学, 2020, 42(1): 63-79.
[4]李枝枝, 柯艺芬, 储日升, 张怀. 二阶锥线性互补问题的广义模系矩阵分裂迭代算法[J]. 计算数学, 2019, 41(4): 395-405.
[5]戴平凡, 李继成, 白建超. 解线性互补问题的预处理加速模Gauss-Seidel迭代方法[J]. 计算数学, 2019, 41(3): 308-319.
[6]李郴良, 田兆鹤, 胡小媚. 一类弱非线性互补问题的广义模系矩阵多分裂多参数加速松弛迭代方法[J]. 计算数学, 2019, 41(1): 91-103.
[7]刘忠祥, 王翠薇, 王增琦. 求解时谐涡流模型鞍点问题的分块交替分裂隐式迭代算法的改进[J]. 计算数学, 2018, 40(3): 271-286.
[8]骆其伦, 黎稳. 二维Helmholtz方程的联合紧致差分离散方程组的预处理方法[J]. 计算数学, 2017, 39(4): 407-420.
[9]甘小艇, 殷俊锋. 二次有限体积法定价美式期权[J]. 计算数学, 2015, 37(1): 67-82.
[10]曹阳, 陶怀仁, 蒋美群. 鞍点问题的广义位移分裂预条件子[J]. 计算数学, 2014, 36(1): 16-26.
[11]任志茹. 三阶线性常微分方程Sinc方程组的结构预处理方法[J]. 计算数学, 2013, 35(3): 305-322.
[12]范斌, 马昌凤, 谢亚君. 求解非线性互补问题的一类光滑Broyden-like方法[J]. 计算数学, 2013, 35(2): 181-194.
[13]曹阳, 谈为伟, 蒋美群. 广义鞍点问题的松弛维数分解预条件子[J]. 计算数学, 2012, 34(4): 351-360.
[14]张丽丽. 关于线性互补问题的模系矩阵分裂迭代方法[J]. 计算数学, 2012, 34(4): 373-386.
[15]豆铨煜, 殷俊锋. 一类求解鞍点问题的广义不精确Uzawa方法[J]. 计算数学, 2012, 34(1): 37-48.

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=197
相关话题/数学 计算 推荐 阅读 结构