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| 试探算法与SSOR预处理共轭梯度算法的拟最佳因子 | |
| 引用本文： | 彭小飞,向淑晃,黎稳.试探算法与SSOR预处理共轭梯度算法的拟最佳因子[J].高等学校计算数学学报,2007,29(2):176-185. |
| 作者姓名： | 彭小飞 向淑晃 黎稳 |
| 作者单位： | 1. 华南师范大学数学科学学院,广州,510631;华南师范大学南海学院数学系,佛山,528225 2. 中南大学数学科学与计算技术学院,长沙,410083 3. 华南师范大学数学科学学院,广州,510631 |
| 基金项目： | 国家自然科学基金资助项目(10671077)，广东省自然科学基金资助项目(06025061)． |
| 摘 要： | 1引言在求解系数矩阵为对称正定的大型线性代数方程组Au=b (1．1)的迭代法方面,七十年代以来发展了各种预处理共轭梯度法．由于SSOR分裂中具有对称因子,可用于加速共轭梯度法,称为SSOR预处理共轭梯度法(简记为;SSORPCG．同时,由于当松弛因子ω∈(0,2)时,SSOR迭代法收敛,从而进一步发展了m步SSOR预处理共轭梯度法(简记为:m-step SSORPCG．胡家赣证明,经过最优的SSOR预条件,预优 |
| 关 键 词： | 试探算法 SSOR预处理 共轭梯度算法 拟最佳因子 |
| 修稿时间： | 2005-11-09 |
THE TEST ALGORITHM AND THE QUASI-OPTIMUM FACTOR OF SSORPCG |
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| Peng Xiaofei,Xiang Shuhuang,Li Wen.THE TEST ALGORITHM AND THE QUASI-OPTIMUM FACTOR OF SSORPCG[J].Numerical Mathematics A Journal of Chinese Universities,2007,29(2):176-185. | |
| Authors: | Peng Xiaofei Xiang Shuhuang Li Wen |
| Affiliation: | School of Mathematical Sciences, South China Normal University, Guangzhou 510631; Dept. of Math., Nanhai College of South China Normal University, Foshan 528225;College of Mathematical Sciences and Computing Technology, Central South University, Changsha 410083 |
| Abstract: | Based on the condition that SSOR preconditioned conjugated gradient method (namely, SSORPCG)is relatively insensitive to the exact choice of the relaxation factor , this paper provides the test algorithm to predict the quasi-optimum relaxation factor for SSORPCG of the corresponding large linear system by analyzing and testing the small size problems. The quasi-optimum relaxation factor leads to the almost optimum convergent speed.Meantime,the algorithm avoids the difficulty in seeking the optimum relaxation factor in theory. Numerical experiments are presented to verify the efficiency of the algorithm.Finally,it is proved from both theory and experiments that the quasi-optimum relaxation factor defined by the test algorithm is accurate to the kind of problem with the optimum relaxation factor irrelated to the scale. |
| Keywords: | test algorithm optimum relaxation factor quasi-optimum relaxation factor ssorpcg |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |
