| 求解大型稀疏矩阵广义特征值的子空间迭代法加速研究 |
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| 引用本文： | 林庚浩,万福磊,黄吉锋.求解大型稀疏矩阵广义特征值的子空间迭代法加速研究[J].北京理工大学学报,2014,34(S1):40-43. |
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| 作者姓名： | 林庚浩 万福磊 黄吉锋 |
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| 作者单位： | 中国建筑科学研究院 建研科技股份有限公司, 北京 100013;中国建筑科学研究院 建研科技股份有限公司, 北京 100013;中国建筑科学研究院 建研科技股份有限公司, 北京 100013 |
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| 基金项目： | 中国建筑科学研究院基础研究课题资助项目(20140122330710029) |
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| 摘 要： | 采用Wilson移频策略对子空间迭代法进行了加速. 为加速高阶特征值的收敛,对Wilson移频策略进行了改进,给出了详细的移频子空间迭代求解特征值的步骤,讨论了若干移频控制参数的选取. 从给出的对比算例可看出,采用移频算法,子空间迭代法求解特征值明显加速,且随着待求特征值阶数的增加,加速效果更加明显,求解时间与待求特征值数近似成线性关系.
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| 关 键 词： | 广义特征值问题 子空间迭代法 移频算法 |
| 收稿时间： | 2014/3/23 0:00:00 |
Accelerated Subspace Iteration Method of Solving Generalized Eigenvalue Problem on Large Sparse Matrix |
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| LIN Geng-hao,WAN Fu-lei and HUANG Ji-feng.Accelerated Subspace Iteration Method of Solving Generalized Eigenvalue Problem on Large Sparse Matrix[J].Journal of Beijing Institute of Technology(Natural Science Edition),2014,34(S1):40-43. |
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| Authors: | LIN Geng-hao WAN Fu-lei and HUANG Ji-feng |
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| Institution: | CABR Technology Co., Ltd, China Academy of Building Research, Beijing 100013, China;CABR Technology Co., Ltd, China Academy of Building Research, Beijing 100013, China;CABR Technology Co., Ltd, China Academy of Building Research, Beijing 100013, China |
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| Abstract: | In this paper, Wilson shift algorithm was employed to accelerate subspace iteration method, the detailed steps were listed and several control parameters were discussed. The results show that the subspace iteration method is accelerated obviously especially with the eigenvalue order increasing. The time need to solve the generalized eigenvalue problem on large sparse matrix is approximately linearly proportional to the number of eigenvalues. |
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| Keywords: | generalized eigenvalue problem subspace iteration method shift algorithm |
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