计算Hamilton矩阵特征值的一个稳定的有效的保结构的算法

闫庆友; 熊西文

计算Hamilton矩阵特征值的一个稳定的有效的保结构的算法

闫庆友^1,2,
熊西文¹

1.
大连大学, 先进设计技术中心, 大连, 116622;
2.
山东财政学院, 经济统计系, 济南, 250014

基金项目: 国家重点基础研究项目(G1999032805);博士点科研基金资助项目;教育部优秀年轻教师基金资助项目

详细信息

作者简介:
闫庆友(1963- ),男,山东茌平人,副教授,博士(E-mail:yanqingyou@263.net).

中图分类号: O241.6
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- 被引次数: 0
出版历程
- 收稿日期: 2001-02-27
- 修回日期: 2002-06-28
- 刊出日期: 2002-11-15

An Effcient and Stable Structure Preserving Algorithm for Computing the Eigenvalues of a Hamiltonian Matrix

YAN Qing-you^1,2,
XIONG Xi-wen¹

1.
Center of Advanced Design Technology, Dalian University, Dalian 116622 P R China;
2.
Department of Economics and Statistics, Shandong Finance Institute, Jinan 250014, P R China

摘要

摘要: 提出了一个稳定的有效的保结构的计算Hamilton矩阵特征值和特征不变子空间的算法,该算法是由SR算法改进变形而得到的。在该算法中,提出了两个策略,一个叫做消失稳策略,另一个称为预处理技术。在消失稳策略中,通过求解减比方程和回溯彻底克服了Bunser Gerstner和Mehrmann提出的SR算法的严重失稳和中断现象的发生,两种策略的实施的代价都非常低。数值算例展示了该算法比其它求解Hamilton矩阵特征问题的算法更有效和可靠。
- Hamilton矩阵 /
- QR型算法 /
- 特征值 /
- 稳定性 /
- 消失稳措施 /
- 回溯技术 /
- 减比
Abstract: An efficient and stable structure preserving algorithm,which is a variant of the QR like (SR)algorithm due to Bunse-Gerstner and Mehrmann,is presented for computing the eigenvalues and stable invariant subspaces of a Hamiltonian matrix.In the algorithm two strategies are employed,one of which is called dis-unstabilization technique and the other is preprocessing technique.Together with them,a socalled ratio-reduction equation and a backtrack technique are introduced to avoid the instability and breakdown in the original algorithm.It is shown that the new algorithm can overcome the instability and breakdown at low cost.Numerical results have demonstrated that the algorithm is stable and can compute the eigenvalues to very high accuracy.
- Hamiltonian matrix /
- QR like algorihm /
- eigenvalue /
- stability /
- dis-unstabilization /
- backtrack technique /
- ratio-reduction

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参考文献(19)

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