RAYLEIGH-RITZ APPROXIMATION FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM | |
Zhang, Lei-Hong1; Xue, Jungong2; Li, Ren-Cang3 | |
刊名 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
![]() |
2014 | |
卷号 | 35期号:2页码:765-782 |
关键词 | linear response eigenvalue problem eigenvalue approximation Rayleigh-Ritz approximation canonical angles deflating subspace error bounds |
ISSN号 | 0895-4798 |
DOI | 10.1137/130946563 |
英文摘要 | Large scale eigenvalue computation is about approximating certain invariant subspaces associated with the interesting part of the spectrum, and the interesting eigenvalues are then extracted through projecting the problem through approximate invariant subspaces into a much smaller eigenvalue problem. In the case of the linear response eigenvalue problem (aka the random phase eigenvalue problem), it is the pair of deflating subspaces associated with the first few smallest positive eigenvalues that needs to be computed. This paper is concerned with approximation accuracy relationships between a pair of approximate deflating subspaces and approximate eigenvalues extracted by the pair. Lower and upper bounds on eigenvalue approximation errors are obtained in terms of canonical angles between an exact and computed pair of deflating subspaces. These bounds can also be interpreted as lower/upper bounds on the canonical angles in terms of eigenvalue approximation errors. They are useful in analyzing numerical solutions to linear response eigenvalue problems. |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | SIAM PUBLICATIONS |
WOS记录号 | WOS:000338830100023 |
内容类型 | 期刊论文 |
源URL | [http://10.2.47.112/handle/2XS4QKH4/1846] ![]() |
专题 | 上海财经大学 |
通讯作者 | Zhang, Lei-Hong |
作者单位 | 1.Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China; 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China; 3.Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA |
推荐引用方式 GB/T 7714 | Zhang, Lei-Hong,Xue, Jungong,Li, Ren-Cang. RAYLEIGH-RITZ APPROXIMATION FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2014,35(2):765-782. |
APA | Zhang, Lei-Hong,Xue, Jungong,&Li, Ren-Cang.(2014).RAYLEIGH-RITZ APPROXIMATION FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,35(2),765-782. |
MLA | Zhang, Lei-Hong,et al."RAYLEIGH-RITZ APPROXIMATION FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 35.2(2014):765-782. |
个性服务 |
查看访问统计 |
相关权益政策 |
暂无数据 |
收藏/分享 |
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。
修改评论