| 求解大型对称特征值问题的改进的块Davidson方法 |
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| 引用本文： | 吕良福,孙济洲,戴华,何丕廉.求解大型对称特征值问题的改进的块Davidson方法[J].天津大学学报(自然科学与工程技术版),2007,40(5):559-562. |
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| 作者姓名： | 吕良福 孙济洲 戴华 何丕廉 |
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| 作者单位： | [1]天津大学理学院,天津300072 [2]天津大学计算机科学与技术学院,天津300072 [3]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;天津市科技攻关项目 |
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| 摘 要： | 块Davidson方法是求解大型对称矩阵特征值问题的一种有效方法．但对一些特征值问题，当Ritz值收敛以后，该方法并不能保证Ritz向量也同时收敛．因此，为加速块Davidson方法的收敛性，研究了块Davidson方法的重新开始技术，将精化策略和收缩技术应用于块Davidson方法，提出了收缩的精化块Davidson方法．数值试验结果及理论分析均表明，新方法比块Davidson和块Lanczos方法有更好的收敛效果，对计算大型对称矩阵的一些极端特征对是有效的．
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| 关 键 词： | 对称矩阵 特征值 块Davidson方法 精化策略 收缩技术 |
| 文章编号： | 0493-2137（2007）05-0559-04 |
| 修稿时间： | 2006-10-102006-12-21 |
Improved Block Davidson Method for Solving Large Symmetric Eigenproblems |
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| L Liang-fu,SUN Ji-zhou,DAI Hua,HE Pi-lian.Improved Block Davidson Method for Solving Large Symmetric Eigenproblems[J].Journal of Tianjin University(Science and Technology),2007,40(5):559-562. |
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| Authors: | L Liang-fu SUN Ji-zhou DAI Hua HE Pi-lian |
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| Institution: | 1. School of Sciences, Tianjin University, Tianjin 300072, China ; 2. School of Computer Science and Technology, Tianjin University, Tianjin 300072, China; 3. School of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
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| Abstract: | Block Davidson method is effective for computing the eigenvalues of large symmetric matrices. However, the corresponding Ritz vectors obtained by block Davidson method always converge more slowly than the Ritz values. In order to solve this problem, a refined block Davidson method with deflation was proposed, which combines refined strategy and deflation technique with block Davidson method. Numerical experiments show that the new algorithm proposed is much more efficient than block Davidson and Lanczos algorithms in improving convergency and calculating extreme eigenpairs of large symmetric matrices. |
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| Keywords: | symmetric matrix eigenvalue block Davidson method refined strategy deflation technique |
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