留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

病态代数系统求解的精细迭代方法

张文志 黄培彦

张文志, 黄培彦. 病态代数系统求解的精细迭代方法[J]. 应用数学和力学, 2013, 34(7): 736-741. doi: 10.3879/j.issn.1000-0887.2013.07.008
引用本文: 张文志, 黄培彦. 病态代数系统求解的精细迭代方法[J]. 应用数学和力学, 2013, 34(7): 736-741. doi: 10.3879/j.issn.1000-0887.2013.07.008
ZHANG Wen-zhi, HUANG Pei-yan. Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations[J]. Applied Mathematics and Mechanics, 2013, 34(7): 736-741. doi: 10.3879/j.issn.1000-0887.2013.07.008
Citation: ZHANG Wen-zhi, HUANG Pei-yan. Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations[J]. Applied Mathematics and Mechanics, 2013, 34(7): 736-741. doi: 10.3879/j.issn.1000-0887.2013.07.008

病态代数系统求解的精细迭代方法

doi: 10.3879/j.issn.1000-0887.2013.07.008
基金项目: 国家自然科学基金(重点)资助项目(11132004;51078145)
详细信息
    作者简介:

    张文志(1982—),男,安徽人,博士(E-mail:cheungmanchi@126.com);黄培彦(1952—),汉族,男,广东人,博士,教授,博士生导师(通讯作者. Tel:+86-20-87114460;E-mail: pyhuang@scut.edu.cn).

  • 中图分类号: O241.5;O302

Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations

  • 摘要: 提出了病态代数系统求解的精细迭代方法.首先利用一个小参数对病态矩阵加以改良,将原病态系统的求解问题转化为该改良系统的求解问题.然后利用精细积分法给出了改良矩阵求逆的高精度方法.该方法具有高精度、高效率的优点,且对改良参数的适应性较好,具有良好的应用前景.理论和数值分析证明了该方法的有效性.
  • [1] Martin R S, Peters G, Wilkinson J H. Symmetric decompositions of a positive definite matrix[J].Numer Math,1965, 7(5): 362-383.
    [2] Martin R S, Peters G, Wilkinson J H. Iterative refinement of the solution of a positive definite system of equations[C]//Baner F L ed.Handbook for Automatic Computation.Vol II.Linear Algebra. Berlin: Springer, 1971.
    [3] Skeel R D. Iterative refinement implies numerical stability for Gaussian elimination[J].Math Comp,1980, 35(151): 817-832.
    [4] Nicholas J H. Iterative refinement enhances the stability of QR factorization methods for solving linear equations[J].BIT,1991, 31(3): 447-468.
    [5] Nicholas J H. Iterative refinement for linear systems and LAPACK[J].IMA J Numer Anal,1997, 17(4): 495-509.
    [6] WU Xin-yuan, SHAO Rong, ZHU Yi-ran. New iterative improvement of a solution for an ill-conditioned system of linear equations based on a linear dynamics system[J].Computers and Mathematics With Applications,2002, 44(8/9): 1109-1116.
    [7] WU Xin-yuan, SHAO Rong, XUE Guo-he. Iterative refinement of solution with biparameter for solving illconditioned systems of linear algebraic equations[J].Applied Mathematics and Computation,2002, 131(2/3): 235-244.
    [8] WU Xin-yuan. An effective predictor-corrector process for large scale linear system of equations[J].Applied Mathematics and Computation,2006, 1(180): 160-166.
    [9] WU Xin-yuan, FANG Yong-lei. Wilkinson’s iterative refinement of solution with automatic step-size control for linear system of equations[J].Applied Mathematics and Computation,2007, 193(2): 506-513.
    [10] ZHONG Wan-xie, Williams F W. A precise time step integration method[J].Journal of Mechanical Engineering Science,1994, 208(6): 427-430.
    [11] 邹积麟, 钱稼如. 病态方程的复合结构解法. 清华大学学报(自然科学版), 2001, 41(4/5): 231-234.(ZOU Ji-lin, QIAN Jia-ru. Composite structure method for ill-conditioned linear equations[J].Journal of Tsinghua University(Science and Technology),2001, 41(4/5): 231-234. (in Chinese))
  • 加载中
计量
  • 文章访问数:  1668
  • HTML全文浏览量:  162
  • PDF下载量:  1363
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-05-20
  • 修回日期:  2013-06-03
  • 刊出日期:  2013-07-15

目录

    /

    返回文章
    返回