RAYLEIGH-RITZ APPROXIMATION FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM

doi:10.1137/130946563

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	RAYLEIGH-RITZ APPROXIMATION FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM
	Zhang, Lei-Hong 1; Xue, Jungong 2; Li, Ren-Cang 3
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.