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对称正定矩阵多级分裂预处理子

Multistage Splitting Preconditioners for Symmetric Positive Definite Linear Systems
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摘要 本文基于对称正定矩阵的多级分裂,讨论了这类方程组的多级分裂预处理子的构造,证明了预处理子的合理性.数值试验显示我们的预处理子是有效的. A new preconditioner for symmetric positive definite linear systems is constructed based on the multistage splitting of the coefficient matrix. The validity of the new preeonditioner is showed and a numerical example is given to illustrate it. Numerical experimentations show that our preconditioners are effective.
作者 徐波 鲁雪晶 张月兰 郭国超 刘仲云
机构地区 长沙理工大学数学与计算科学学院
出处 《数学理论与应用》 2013年第1期57-62,共6页 Mathematical Theory and Applications
关键词 预处理子 多级分裂 对称正定 共轭梯度法 Preconditioner Multistage Splitting Symmetric Positive Definite Conjugate Gradient Method
分类号 O241.6 [理学—计算数学]
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参考文献6

  • 1P. J. Lanzkron, D. J. Rose, D. B. Szyld,Convergence of nested classical iterative methods for linear systems, Numerische Mathematik, 58 : 685 - 702, 1991.
  • 2Z. H. Cao, Convergence of nested iterative methods for symmetric P- regular splitting, SIAM, Matrix Anal. Appl., 22( 1 ): 20- 32, 2000.
  • 3R. H. ehan and M. K. Ng, Coniugate Gradient Methods For Toeplitz Systems, SLAM, 38(3): 427 -482, 1996.
  • 4Gene H. Golub and Charles F. Van Loan, Matrix Computations, Turing,2011.
  • 5刘仲云,刘成志,张育林.对称正定Toeplitz方程组的多级迭代求解[J].计算数学,2012,34(4):397-404. 被引量：2
  • 6鲁雪晶,刘仲云,张育林.对称正定矩阵的多级迭代法[J].数学理论与应用,2013,33(1):7-12. 被引量：1

二级参考文献14

  • 1Bai Zhong-Zhi. The convergence of the two-stage iterative method for hermitian positive definite linear systems[J]. Appl. Math. Lett. 1998, 11(2): 1-5.
  • 2Bai Zhong-Zhi. A class of two-stage iterative methods for systems of weakly nonlinear equations[J]. Numer. Algorithms, 1997, 14: 295-319.
  • 3Bai Zhong-Zhi, Wang De-Ren. The monotone convergence of the two-stage iterative method for solving large spares systems of linear equations[J]. Appl. Math. Lett. 1997, 10(1): 113-117.
  • 4Bai Zhong-Zhi. Convergence analysis of the two-stage multisplitting method[J]. Calcolo, 1999, 36(2): 63-74.
  • 5Cao Zhi-Hao. Convergence of nested iterative methods for symmetric P-regular splittings[J]. SIAM J. Matrix Anal. ADD1. 2000. 22(1): 20-32.
  • 6Chan Raymond H, Ng Micheal K. Conjugate gradient methods for Toeplitz systems[J]. SIAM Rev. 1996, 38: 427-482.
  • 7Frommer Andreas, Szyld Daniel B. H-Splittings and two-stage iterative methods[J]. Numer. Math. 1992, 63: 345-356.
  • 8Colub Gene H, Van Loan Charles F. Matrix Computation. Third Edition. The Johns Hopkins University Press, 1996.
  • 9Lanzkron Paul J, Rose Donald J, Szyld Daniel B. Convergence of nested classical iterative methods for linear systems[J]. Numer. Math. 1991, 58: 685-702.
  • 10Liu Zhongyun, Wu Hebin, Lin Lu. The two-stage iterative methods for symmetric positive definite matrices[J1. Aopl. Math. Comput. 2000, 114: 1-12.

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数学理论与应用
2013年 第1期

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