| 带极端特征向量的重新开始GMRES算法 |
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| 引用本文： | 王正盛,钟宝江. 带极端特征向量的重新开始GMRES算法[J]. 南京航空航天大学学报, 1999, 31(4): 447-451 |
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| 作者姓名： | 王正盛 钟宝江 |
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| 作者单位： | 南京航空航天大学理学院,南京,210016 |
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| 基金项目： | 国家自然科学基金,江苏省自然科学基金 |
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| 摘 要： | 求解大型非对称线性方程组的 Ｇ Ｍ Ｒ Ｅ Ｓ算法通常以其重新开始版本来减少存储量和计算量，而重新开始过程将影响残量的收敛速度。由此可以考虑在重新开始时保留一些重要信息，如把极端特征值对应的近似特征向量加到新的 Ｋｒｙｌｏｖ 子空间中。这样可以大大加快其收敛速度，而且保持残量最小化性质。
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| 关 键 词： | 线性系统 迭代法 Krylov子空间 |
A Restarted GMRES Method Augmented with Extreme Eigenvectors |
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| Wang Zhengsheng,Zhong Baojiang. A Restarted GMRES Method Augmented with Extreme Eigenvectors[J]. Journal of Nanjing University of Aeronautics & Astronautics, 1999, 31(4): 447-451 |
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| Authors: | Wang Zhengsheng Zhong Baojiang |
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| Abstract: | GMRES method for solving unsymmetric linear systems is generally used with restarting to reduce storage and orthogonalization cost. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restarting. It is suggested that approximate eigenvectors corresponding to a few of the extreme eigenvalues are formed and are added to the subspace for GMRES. The convergence can be much faster, and the minimal residual property is retained. |
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| Keywords: | linear systems iteration method Krylov subspace |
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