| 哈密尔顿矩阵特征谱问题的辛算法 |
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| 引用本文： | 丁克伟. 哈密尔顿矩阵特征谱问题的辛算法[J]. 合肥工业大学学报(自然科学版), 2000, 23(3) |
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| 作者姓名： | 丁克伟 |
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| 作者单位： | 大连理工大学,工程力学系,辽宁,大连,116023 |
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| 基金项目： | 国家自然科学基金资助项目! (1 9392 30 5),安徽省教委基金资助项目 !(99j1 o2 2 6zc) |
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| 摘 要： | 文章基于前人的工作 ,在哈密尔顿矩阵约化过程中 ,采用了辛相似变换 ,使得哈密尔顿矩阵在辛相似变换下仍保持Hamilton结构 ,这样从根本上确保了特征值的正确性和稳定性 ,也能保证特征值成对出现且在每个半平面上都只求得 n个特征值 ,不至于出现特征值在小扰动下跨过虚轴的混乱局面
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| 关 键 词： | 辛算法 哈密尔顿矩阵 辛相似变换 特征问题 |
The symplectic algorithm method for Hamiltonian matrix eigen problem |
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| DING Ke-wei. The symplectic algorithm method for Hamiltonian matrix eigen problem[J]. Journal of Hefei University of Technology(Natural Science), 2000, 23(3) |
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| Authors: | DING Ke-wei |
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| Abstract: | The symplectic algorithm method for Hamiltonian matrix eigenvalue and eigenvector problem is presented based upon predecessors' papers. This method works with symplectic similarity transformation which reflects the structure of the spectrum of Hamiltonian matrices, and has a higher numerical accuracy than ordinary algorithm.It is therefore guaranteed that the computed eigenvalues occur in plus minus pairs and ensure numerical stabilities.This algorithm can find exactly n eigenvalues in each half plane. Even small perturbations may not cause the computed eigenvalues to cross the imaginary axis. |
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| Keywords: | symplectic algorithm Hamiltonian matrix symplectic similarity transformation eigen problem |
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