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BunserGerstner和Mehrmann提出的SR算法的严重失稳和中断现象的发生。
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 so called 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.
出处
《应用数学和力学》
CSCD
北大核心
2002年第11期1150-1168,共19页
Applied Mathematics and Mechanics
基金
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
关键词
HAMILTON矩阵
QR型算法
特征值
稳定性
消失稳措施
回溯技术
Hamiltonian matrix
QR like algorihm
eigenvalue
stability
dis_unstabilization
backtrack technique
ratio_reduction
