计算Hamilton矩阵特征值的一个稳定的有效的保结构的算法  

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

作　　者：闫庆友[1] 熊西文[1] 

机构地区：[1]大连大学先进设计技术中心

出　　处：《应用数学和力学》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

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.

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 

分 类 号：O241.6[理学—计算数学]