| 引用本文： |
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吴果林,王晟.误差向量与Krylov子空间对GMRES(m)算法收敛速度的影响[J].广西科学,2011,18(3):214-217,221. [点击复制]
- WU Guo-lin,WANG Sheng.Influence of Residual Vector and Krylov Subspace on Convergence Velocity of GMRES Algorithm[J].Guangxi Sciences,2011,18(3):214-217,221. [点击复制]
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| 摘要: |
| 从广义极小残量法GMRES (m)的结构出发,分析其误差向量与Krylov子空间对该算法收敛速度的影响,推导出误差向量与Krylov子空间第1个向量和第m+1个向量的方向余弦关系,并用数值算例验证其合理性.当误差向量rk+1在Krylov子空间向量v1的投影较大而在向量vm+1的投影较小时,GMRES (m)算法收敛速度较慢,反之亦反.算例结果与理论结果相符. |
| 关键词: 线性方程 迭代方法 广义极小残量法 Krylov子空间 |
| DOI： |
| 投稿时间：2011-01-30修订日期：2011-03-07 |
| 基金项目:2008年桂林航天工业高等专科学校科研项目资助 |
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| Influence of Residual Vector and Krylov Subspace on Convergence Velocity of GMRES Algorithm |
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WU Guo-lin1, WANG Sheng2
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| (1.Department of Computer, Guilin College of Aerospace Techology, Guilin, Guangxi, 541004, China;2.School of Mathematics & Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China) |
| Abstract: |
| By analysing the structure of restarted GMRES algorithm, we discover that residual vector and Krylov subspace have an influence on the convergence velocity of GMRES (m) algorithm, and deduce that the residual vector has a direction cosine relationship with the first vector and m+1 vector in Krylov subspace.A numerical example is used to verify its rationality.Algorithm analysis indicates that the convergence velocity of GMRES (m)method is slower when the project of the residual vector rk+1 is large in the krylov subspace v1 vector and small in the krylov subspace vm+1 vector, or vice versa. |
| Key words: linear equation iterative method GMRES (m) Krylov subspace |
