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| 红黑排序混合算法收敛速度分析 | |
| 引用本文： | 杭旭登,刘兴平,袁光伟,宋杰.红黑排序混合算法收敛速度分析[J].计算数学,2003,25(4):423-434. |
| 作者姓名： | 杭旭登 刘兴平 袁光伟 宋杰 |
| 作者单位： | 1. 中国工程物理研究院研究生部,北京,100088 2. 北京应用物理与计算数学研究所计算物理实验室,北京,100088 3. 石油勘探开发研究院,北京,100083 |
| 基金项目： | 国家重点基础研究专向经费(G1999032801，G1999022512)，国家基金委重点基金(19932010) |
| 摘 要： | The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods. |
| 关 键 词： | 循环矩阵 泊松方程 收敛性 偏微分方程 稀疏线性方程组 红黑排序混合算法 |
| 修稿时间： | 2001年8月6日 |
A CONVERGENCE RATE ANALYSIS OF HYBRID RED-BLACK ORDERING ALGORITHM |
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| Hang Xudeng Graduate School of CAEP,Beijing, Liu Xingping Yuan Guangwei Laboratory of Computational Physics,IAPCM,Beijing, Song Jie Academy of Oil Development and Exploiture,Beijing.A CONVERGENCE RATE ANALYSIS OF HYBRID RED-BLACK ORDERING ALGORITHM[J].Mathematica Numerica Sinica,2003,25(4):423-434. | |
| Authors: | Hang Xudeng Graduate School of CAEP Beijing Liu Xingping Yuan Guangwei Laboratory of Computational Physics IAPCM Beijing Song Jie Academy of Oil Development and Exploiture Beijing |
| Institution: | Hang Xudeng Graduate School of CAEP, Beijing, 100088 Liu Xingping Yuan Guangwei Laboratory of Computational Physics, IAPCM, Beijing, 100088 Song Jie Academy of Oil Development and Exploiture, Beijing, 100083 |
| Abstract: | The algorithm of applying the block Gauss elimination to the Red-Black ordering matrix to reduce the order of the system then solve the reduced system by iterative methods is called Hybrid Red-Black Ordering algorithm. In this paper, we discuss the convergence rate of the hybrid methods combined with JACOBI, CG, GMRES(m). Theoretical analysis shows that without preconditioner these three hybrid methods converge about 2 times as fast as the corresponding natural ordering methods. For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m). Various numerical experiments are presented. For large scale problem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural ordering methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods. |
| Keywords: | Hybrid Red-Black Ordering Algorithm Poisson Equation Schur Complement Iterative Method Convergence Rate |
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