华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (2): 1-6,55.doi: 10.3969/j.issn.1000-5641.2019.02.001

• 数学 •    下一篇

严格次对角占优线性方程组迭代法的收敛性分析

蔡静1,2   

  1. 1. 东南大学 数学学院, 南京 211189;
    2. 湖州师范学院 理学院, 浙江 湖州 313000
  • 收稿日期:2018-04-02 出版日期:2019-03-25 发布日期:2019-03-27
  • 作者简介:蔡静,女,副教授,研究方向为数值代数.E-mail:caijing@zjhu.edu.cn.
  • 基金资助:
    国家自然科学基金（11771076）；中国博士后基金（2016M601688）

Convergence analysis of iterative methods for strictly sub-diagonally dominant linear equations

CAI Jing1,2   

  1. 1. School of Mathematics, Southeast University, Nanjing 211189, China;
    2. College of Science, Huzhou University, Huzhou Zhejiang 313000, China
  • Received:2018-04-02 Online:2019-03-25 Published:2019-03-27

RichHTML

18

PDF

517

摘要： Jacobi迭代法、Guass-Seidel迭代法和SOR迭代法是求解线性方程组的常用迭代方法.本文证明了系数矩阵严格次对角占优时，Jacobi迭代法、Guass-Seidel迭代法和SOR迭代法均收敛，并给出了相应的误差估计.通过比较三种迭代法的误差上界，指明Guass-Seidel迭代法的误差上界最小.

关键词: 线性方程组, 迭代法, 严格次对角占优, 误差上界

Abstract: The Jacobi iterative method, Guass-Seidel iterative method, and SOR iterative method are commonly used in solving linear equations. When the coefficient matrix of a system of linear equations is strictly sub-diagonally dominant, we demonstrate that the Jacobi, Guass-Seider, and SOR iterative methods are all convergent. By comparing the upper bounds of error for the three iterative methods, we show that the upper bound of error for the Guass-Seidel iterative method is minimal.

Key words: linear equations, iterative method, strictly sub-diagonally dominant, error bounds

中图分类号: