RIEMANNIAN NEWTON METHOD FOR THE MULTIVARIATE EIGENVALUE PROBLEM

doi:10.1137/100788975

CORC > 上海财经大学 > 上海财经大学

	RIEMANNIAN NEWTON METHOD FOR THE MULTIVARIATE EIGENVALUE PROBLEM
	Zhang, Lei-Hong
刊名	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
	2010
卷号	31 期号:5 页码:2972-2996
关键词	multivariate statistics canonical correlation multivariate eigenvalue problem Riemannian Newton method Rayleigh quotient iteration precondition Krylov subspace methods power method quadratic convergence global convergence
ISSN号	0895-4798
DOI	10.1137/100788975
英文摘要	The multivariate eigenvalue problem (MEP) which originally arises from the canonical correlation analysis is an important generalization of the classical eigenvalue problem. Recently, the MEP also finds applications in many other areas and continues to receive interest. However, the existing algorithms for the MEP are the generalization of the power iteration for the classical eigenvalue problem and converge slowly. In this paper, we propose a Riemannian Newton method for the MEP, which is a generalization of the classical Rayleigh quotient iteration (RQI). Under a mild condition, the local quadratic convergence can be guaranteed. We also develop the inexact implementation by employing some Krylov subspace method and establishing the preconditioning technique to obtain an inexact Riemannian Newton step efficiently. Preliminary but promising numerical experiments are reported which show a good convergence performance in terms of the proposed method's speed and global convergence.
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000285933400037
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2922]
专题	上海财经大学
通讯作者	Zhang, Lei-Hong
作者单位	Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Lei-Hong. RIEMANNIAN NEWTON METHOD FOR THE MULTIVARIATE EIGENVALUE PROBLEM[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2010,31(5):2972-2996.
APA	Zhang, Lei-Hong.(2010).RIEMANNIAN NEWTON METHOD FOR THE MULTIVARIATE EIGENVALUE PROBLEM.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,31(5),2972-2996.
MLA	Zhang, Lei-Hong."RIEMANNIAN NEWTON METHOD FOR THE MULTIVARIATE EIGENVALUE PROBLEM".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 31.5(2010):2972-2996.