解线性方程组的预条件Gauss-Seidel型迭代法

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

基金项目: 教育部“新世纪人才支持计划”基金资助项目(2004);四川省应用基础研究基金资助项目(05JY029-068-2)

Preconditioned Gauss-Seidel Type Iterative Methods for Solving Linear Systems

School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China

摘要: 给出了解线性方程组的预条件Gauss-Seidel型方法,提出了选取合适的预条件因子．并讨论了对Z-矩阵应用这种方法的收敛性,给出了收敛最快时的系数取值．最后给出数值例子，说明选取合适的预条件因子应用Gauss-Seidel方法求解线性方程组是有效的．
- Gauss-Seidel方法 /
- 预条件迭代法 /
- Z-矩阵
Abstract: The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, was presented. Convergence of the preconditioned method applied to Z-matrices was discussed. Also the optimal parmeter was presented. Numerical results show that the proper choice of the preconditioner can lead to effective the preconditioned Gauss-Seidel type iterative methods for solving linear systems.
- Gauss-Seidel method /
- preconditioned iterative method /
- Z-matrix

[1]	LI Wen.Preconditioned AOR iterative methods for linear systems[J].Internat J Computer Math,2002,79(1):89—101. doi: 10.1080/00207160211910
[2]	Young D M.Iterative Solution of Large Linear Systems[M].New York: Academic Press,1971.
[3]	Varga R S.Matrix Iterative Analysis[M].Englewood Cliffs, NJ: Prentice-Hall,1981.
[4]	Berman A,Plemmons R J.Nonnegative Matrices in the Mathematical Sciences[M],London:Academic Press, 1979.
[5]	Hans Schneider. Which depend on graph structure[J].Linear Algebra Appl,1984,58:407—424. doi: 10.1016/0024-3795(84)90222-2
[6]	Evans D J,Martins M M,Trigo M E.The AOR iterative method for new preconditioned linear systems[J].J Comput Appl Math,2001,132:461—466. doi: 10.1016/S0377-0427(00)00447-7