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

CAI Jing

doi:10.3969/j.issn.1000-5641.2019.02.001

Issue 2

Mar. 2019

Turn off MathJax

Article Contents

Article Navigation > Journal of East China Normal University (Natural Sciences) > 2019 > (2): 1-6, 55

CAI Jing. Convergence analysis of iterative methods for strictly sub-diagonally dominant linear equations[J]. Journal of East China Normal University (Natural Sciences), 2019, (2): 1-6, 55. doi: 10.3969/j.issn.1000-5641.2019.02.001

Citation:

CAI Jing. Convergence analysis of iterative methods for strictly sub-diagonally dominant linear equations[J]. Journal of East China Normal University (Natural Sciences), 2019, (2): 1-6, 55. doi: 10.3969/j.issn.1000-5641.2019.02.001

Citation:

PDF( 430 KB)

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

doi: 10.3969/j.issn.1000-5641.2019.02.001

CAI Jing^{1,2
,}

1.
School of Mathematics, Southeast University, Nanjing 211189, China
2.
College of Science, Huzhou University, Huzhou Zhejiang 313000, China

Received Date: 2018-04-02
Publish Date: 2019-03-25

Abstract

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.
- linear equations,
- iterative method,
- strictly sub-diagonally dominant,
- error bounds

FullText(HTML)

References(11)

References

[1]	韩俊林, 刘建州.广义对角占优矩阵和广义次对角占优矩阵等价条件的注记[J].商丘师范学院学报, 2002, 18(2):46-48. doi: 10.3969/j.issn.1672-3600.2002.02.013
[2]	陈思源. α-次对角占优矩阵与广义严格次对角占优矩阵的判定[J].石河子大学学报, 2006, 24(6):786-789. doi: 10.3969/j.issn.1007-7383.2006.06.034
[3]	张成毅, 李耀堂.弱严格对角占优矩阵非奇异的判定条件[J].工程数学学报, 2006, 23(3):505-510. doi: 10.3969/j.issn.1005-3085.2006.03.017
[4]	崔琦, 宋岱才, 刘晶. Ostrowski对角占优矩阵与非奇异H-矩阵的判定[J].江西师范大学学报(自然科学版), 2007, 31(5):497-499. doi: 10.3969/j.issn.1000-5862.2007.05.014
[5]	LI W, CHEN Y M. Some new two-sided bounds for determinants of diagonally dominant matrices[J]. Journal of Inequalities and Applications, 2012, 2012:61-69. doi: 10.1186/1029-242X-2012-61
[6]	徐屹.严格对角占优矩阵的迭代法[J].武汉理工大学学报, 2008, 30(9):177-180. http://d.old.wanfangdata.com.cn/Periodical/whgydxxb200809047
[7]	宋岱才, 魏晓丽, 赵晓颖. α严格对角占优矩阵与迭代法的收敛性定理[J].辽宁石油化工大学学报, 2010, 30(1):81-83. doi: 10.3969/j.issn.1672-6952.2010.01.022
[8]	HUANG R, LIU J Z, ZHU L. Accurate solutions of diagonally dominant tridiagonal linear systems[J]. BIT Numer Math, 2014, 54:711-727. doi: 10.1007/s10543-014-0481-5
[9]	金玲玲, 苏岐芳.几类特殊矩阵方程组的迭代解法收敛性分析[J].台州学院学报, 2015, 37(6):8-16. http://d.old.wanfangdata.com.cn/Periodical/tzxyxb201506002
[10]	胡家赣.线性代数方程组的迭代解法[M].北京:科学出版社, 1991.
[11]	陈恒新.关于AOR迭代法的研究[J].应用数学与计算数学学报, 2002, 16(1):40-46. doi: 10.3969/j.issn.1006-6330.2002.01.006