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系数矩阵含参数分裂形式的SOR迭代法收敛性分析

Convergence analysis of the SOR iterative method in coefficient matrix splitting with parameters
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摘要 给出预条件方后线性方程组的系数矩阵的一类含参数的分裂形式,使系数矩阵的分裂更加一般化,同时讨论在该形式下的SOR迭代法的收敛性,并与一般的预条件方法进行比较分析,说明这种方法收敛性更好,最后找到参数的最优选取. This paper studies the linear system coefficient matrix splitting with parameters in the preconditioned,and make the matrix splitting more general.Then discuss convergence of the SOR iterative method in this matrix splitting with parameters,and compare with the general preconditioned iterative method,explain this method is better,gives the parameter optimal selection.
作者 王慧勤
机构地区 宝鸡文理学院数学系
出处 《陕西科技大学学报（自然科学版）》 2012年第5期135-138,共4页 Journal of Shaanxi University of Science & Technology
基金 宝鸡文理学院重点基金项目(ZK10110)
关键词 预条件 收敛性 SOR迭代法 谱半径 矩阵分裂 precondition convergence the SOR iteration method spectral radius matrix splitting
分类号 O241.6 [理学—计算数学]
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参考文献6

  • 1Ting Zhu Huang, Guang Hui Cheng, Xiao-Yu Cheng. Modified SOR-type iterative method for Z-matrices[J]. Applied Mathematics and Computation, 2006, 175 (2): 258-268.
  • 2Hiroshi Niki, Kyouji Harada, Munenori Morimoto. 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.
  • 3Jae Heon Yun. A note on the modified SOR method for z- matrices[J]. Applied Mathematics and Computation, ~007,194(3) :572-576.
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  • 6雷刚.预条件(I+S)后改进矩阵分裂的SOR迭代法收敛性分析[J].宝鸡文理学院学报（自然科学版）,2011,31(3):13-17. 被引量：3

二级参考文献11

  • 1Ananda D Gunawardena, S K Jain, Larry Snyder. Modified iterative method for consistent linear systems[J]. Linear Algebra and its Applications, 1991,154-156: 123-143.
  • 2LIU Qing-bing, CHEN Guo-ling, CAI Jing. Convergence analysis of the preconditioned Gauss-Seidel method for H-matrices[J]. Computers & Mathematics with Applications, 2008, 56(8): 2048-2053.
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  • 5DAVID M Yong. Iterative solution of large linear systems[M]. New York:Academic Press, 1971.
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  • 10CAO Zhi--hao, WU He-bing, LIU Zhong-yun. A note on weak splitting of matrices[J]. Applied Mathematics and Computation, 2000,112(2/3) : 265-275.

共引文献2

陕西科技大学学报（自然科学版）
2012年 第5期

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