[1]赵佳宝,盛昭瀚.一种改进的CGS方法[J].东南大学学报(自然科学版),1999,29(3):43-48.[doi:10.3969/j.issn.1001-0505.1999.03.008]
 Zhao Jiabao,Sheng Zhaohan.An Improved Conjugate Gradient Square Algorithm[J].Journal of Southeast University (Natural Science Edition),1999,29(3):43-48.[doi:10.3969/j.issn.1001-0505.1999.03.008]
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一种改进的CGS方法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
29
期数:
1999年第3期
页码:
43-48
栏目:
数学、物理学、力学
出版日期:
1999-05-20

文章信息/Info

Title:
An Improved Conjugate Gradient Square Algorithm
作者:
赵佳宝 盛昭瀚
东南大学经济管理学院,南京 210096
Author(s):
Zhao Jiabao Sheng Zhaohan
College of Econimic and Management, Southeast University,Nanjing 210096
关键词:
Bi-CG CGS Krylov子空间 稀疏矩阵
Keywords:
Bi-CG CGS Krylov subspace sparse matrix
分类号:
O241.6
DOI:
10.3969/j.issn.1001-0505.1999.03.008
摘要:
在分析CGS算法的基础上,提出了采用两个相似的Bi-CG过程,利用Bi-CG过程的迭代中系数与迭代初值密切相关的特点,使其中一个Bi-CG过程的系数保证剩余向量与Krylov子空间Kk(AT,(~overr)0)正交,而另一个Bi-CG过程的迭代系数使得剩余向量与Krylov子空间K′k(AT,(~overs)0)正交,构造出一种新的类似CGS方法的求解大型系数矩阵稀疏线性方程组的迭代算法. 数值实验表明这种算法在一定程度上减小了迭代算法在收敛过程中的剩余向量,从而使得算法具有了更好的稳定性.
Abstract:
After the analysis of the Conjugate Gradient Square(CGS) algorithm, we present a new algorithm to solve the large-scale sparse linear equations in this paper. For the parameters generated by the Bi-CG process are tightly connected with the initial value, so we choose two different initial values with which to begin two different Bi-CG processes. One of them assures the residual vector at each iteration to be orthogonal to the subspace Kk(AT,(~overr)0), the other to the subspace K′k(AT, (~overs)0) accordingly. Numerical experiments show that these variants of the algorithm CGS can work well to lower the norms of the residuals which make the algorithm performs more stable and converge to real solution more smoothly.

参考文献/References:

[1] Saad+ Y.The lanczos bi-orhthogonalization algorithm and other oblique projection methods for solving unsymmetric systems.Siam J Numer Anal,1982,19(3):485~500
[2] Peter Sonneveld.CGS,a fast lanczos-type solver for non-symmetric linear systems.Siam J Stat Comput,1989,10(4):36~52
[3] Vorst H A Van Der.Bi-Cgstab:a fast and smoothy convergening variant of Bi-CG for the solution of nonsymmetric linear systems.Siam J Sci Stat Comput,1992,13(2):631~644
[4] Zhao Zhongyi,Zhang Qiming,Tan Genlin,et al.A new preconditioner for CGS iterarion in solving large nonsymmetric linear equations in semiconductor device simulation.IEEE Tans on CAD,1991,10(11):1432~1440
[5] Parlett B N,Taylor D.A look ahead lanczos algorithm for insymmetric matrices.Mathematics of Computation,1985,44:105~124

备注/Memo

备注/Memo:
第一作者:男,1972年生,博士研究生.
更新日期/Last Update: 1999-05-20