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A riemannian Newton algorithm for nonlinear eigenvalue problems
Zhao Z.1; Bai Z.-J.2; Jin X.-Q.1
2015
Source PublicationSIAM Journal on Matrix Analysis and Applications
ISSN10957162 08954798
Volume36Issue:2Pages:752-774
Abstract

We give the formulation of a Riemannian Newton algorithm for solving a class of nonlinear eigenvalue problems by minimizing a total energy function subject to the orthogonality constraint. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method. Moreover, the positive definiteness condition of the Riemannian Hessian of the total energy function at a solution is derived. Some numerical tests are reported to illustrate the efficiency of the proposed method for solving large-scale problems.

KeywordGrassmann Manifold Nonlinear Eigenvalue Problem Riemannian Newton Algorithm Stiefel Manifold
DOI10.1137/140967994
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000357407800020
PublisherSIAM PUBLICATIONS
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Citation statistics
Cited Times [WOS]:10   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics, University of Macau, Macau, People’s Republic of China
2.School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhao Z.,Bai Z.-J.,Jin X.-Q.. A riemannian Newton algorithm for nonlinear eigenvalue problems[J]. SIAM Journal on Matrix Analysis and Applications,2015,36(2):752-774.
APA Zhao Z.,Bai Z.-J.,&Jin X.-Q..(2015).A riemannian Newton algorithm for nonlinear eigenvalue problems.SIAM Journal on Matrix Analysis and Applications,36(2),752-774.
MLA Zhao Z.,et al."A riemannian Newton algorithm for nonlinear eigenvalue problems".SIAM Journal on Matrix Analysis and Applications 36.2(2015):752-774.
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