广东工业大学学报 ›› 2008, Vol. 25 ›› Issue (4): 44-48.

• 综合研究 • 上一篇    下一篇

一种求解基于GAM离散的线性系统的预处理算子

  

  1. 广东工业大学应用数学学院；
  • 出版日期:2008-03-01 发布日期:2008-03-01

A Block Lower Bidiagonal Preconditioner with GMRES for Systems Derived from Generalized Adams Methods(GAM)

  1. Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510006,China
  • Online:2008-03-01 Published:2008-03-01

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摘要： 对由Generalized Adams Methods(GAM)离散微分方程所得的大型线性系统,提出了一种基于块的二对角矩阵预处理算子,用以配合使用广义极小残量法(GMRES),实现加速求解.收敛性证明和数值实验显示该方法是非常有效的.

关键词: 预处理算子； 边界值方法； 广义亚当斯方法； 广义极小残量法；

Abstract: It introduces a lower block bidiagonal preconditioner with GMRES method for solving the linear systems derived from the GAM is introduced.The theoretical arguments and numerical results are given to illustrate that our method is very effective.

Key words: preconditioner； Boundary Volue Methochs(BVMs)； Generalized Adams Methods(GAM)； Generalized Minimum Residual Linear Equation Solution(GMRES)；

[1] Sun H,,Zhang J.A high-order compact boundary valuemethod for solving one-dimensional heat equations. Numer Meth Part D E . 2003

[2] Bertaccini D.A circulant preconditioner for the systems ofLMF-based ODE codes. SIAM Journal on Scientific Computing . 2000

[3] Gray R M.Toeplitz and circulant matrices:A review. . 2006

[4] Frigo M,Johnson S G. FFTW Web page http:∥www.fftw.org/ . 2007

[5] L. Brugnano,and D. Trigiante.Solving Differential Problems by Multistep Initial and Boundary Value Methods. . 1998

[6] Chan R,Ng M.Conjugate gradient methods for Toeplitz systems. SIAM Review . 1996

[7] Jin X,,Sin V,Song L.Circulant preconditioned WR-BVM methods for ODE systems. Journal of Computational and Applied Mathematics . 2004

[8] Ming-Chao Cai and Xiao-Qing Jin.BCCB preconditioners for solving linear systems from delay differential equations. Computers and Mathematics With Applications . 2005

[9] Chan R,Ng M,Jin X.Strang-type preconditioners for systems of LMF-based ODE codes. IMA Journal of Numerical Analysis . 2001

[10] Y Saad.Iterative methods for sparse linear systems. . 2003

[11] 钟宝江.  GMRES方法的收敛率[J]. 高等学校计算数学学报. 2003(03)

[12] 张贤达著.矩阵分析与应用[M]. 清华大学出版社, 2004

[13] 陈景良,陈向晖著.特殊矩阵[M]. 清华大学出版社, 2001
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