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多分裂形式下的SOR迭代法收敛性分析

Convergence Analysis of the SOR Iterative Method in a Variety of Splitting
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摘要 在预条件方法解大型线性方程组Ax=b时,给出预条件后多种分裂形式的SOR迭代方法,说明这些方法能够使SOR迭代法收敛,并与一般的预条件方法进行比较分析,证明了这些分裂形式加速效果更好。最后用数值例子加以验证。 By using the preconditioned iterative method for solving the linear system Ax = b, the paper gives several types splitting of the SOR iterative method in preconditioned, then proves that these new split methods can accelerate convergence, and explains why the convergence rate is faster than general SOR method. Finally the numerical example is given.
作者 雷刚
机构地区 宝鸡文理学院数学系
出处 《江南大学学报（自然科学版）》 CAS 2012年第1期91-94,共4页 Joural of Jiangnan University (Natural Science Edition)　
基金 国家自然科学基金项目(10071048) 宝鸡文理学院重点项目
关键词 预处理 收敛性 SOR迭代法 precondition, convergence, the SOR iteration method
分类号 O241.6 [理学—计算数学]
  • 相关文献

参考文献7

  • 1WANG Xue-zhong,HUANG Ting-zhu,FU Ying-ding.Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems[J].Journal of Computational and Applied Mathematics,2007,206:726-732.
  • 2HUANG Ting-zhu,CHENG Guang-hui,CHENG Xiao-yu.Modified SOR-type iterative method for Z-matrices[J].AppliedMathematics and Computation,2006,175:258-268.
  • 3Hiroshi Niki,Kyouji Harada,Munenori Morimoto,et al.The survey of preconditioners used for accelerating the rate of conver-gence in the Gauss-Seidel method[J].Journal of Computational and Applied Mathematics,2004,165:587-600.
  • 4Jae Heon Yun.A note on the modified SOR method for Z-matrices[J].Applied Mathematics and Computation,2007,194:572-576.
  • 5Yun J H,Kim S W.Convergrnce of the preconditioned AOR method for irreducible L-matrices[J].Appl Math Comput,2008,201:56-64.
  • 6LI Wen.Comparison results for solving preconditioned linear systems[J].Journal of Compurtational and Applied Mathematics,2005,176:319-329.
  • 7王慧勤,雷刚.预处理后新分裂下的SOR迭代法收敛性讨论[J].安徽大学学报（自然科学版）,2010,34(4):39-43. 被引量：3

二级参考文献10

  • 1Hiroshi N,Kyouji H,Munenori M,et al.The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method[J].Journal of Computational and Applied Mathematics,2004,165(3):587-600.
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  • 4Richard S,Varga A.Matrix iterative analysis[M].Heidelberg:Spring-Verlag,2000.
  • 5Wang X Z,Huang T Z,Fu Y D.Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems[J].Journal of Computational and Applied Mathematics,2007,206(4):726-732.
  • 6Yun J H.Convergence of SSOR multisplitting method for an H-matrix[J].Journal of Computational and Applied Mathematics,2008,217(2):252-258.
  • 7Cao Z H,Wu H B,Liu Z Y,et al.A note on weak splitting of matrices[J].Applied Mathematics and Computation,2000,112(2):265-275.
  • 8Wang Z D,Huang T Z.Comparison result between Jacobi and other iterative methods[J].Journal of Computational and Applied Mathematics,2004,169(1):45-51.
  • 9Wen Li.Comparison results for solving preconditioned linear systems[J].Journal of Computational and Applied Mathematics,2005,176(2):319-329.
  • 10雷刚.两类预条件后迭代法收敛性的讨论[J].东北师大学报（自然科学版）,2009,41(3):21-25. 被引量：5

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江南大学学报（自然科学版）
2012年 第1期

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