full
search.png

Search

close.png

Cancel

arrow
Volume 28, Issue 2
Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem

Xin Huang, Zhaojun Bai & Yangfeng Su

DOI: 10.4208/jcm.2009.10-m1002

J. Comp. Math., 28 (2010), pp. 218-234.

Published online: 2010-04

Preview Full PDF 2656 29197

Cited by

google scholar semantic scholar
Export citation
  • Abstract

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method (SLAM). The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.

  • Keywords

Nonlinear eigenvalue problem, Rank-one modification, Rank-one damping, Low-rank damping, Picard, Successive linear approximation method, Nonlinear Rayleigh quotient iteration, Safeguard, Global convergence.

  • AMS Subject Headings

65F15, 65H17, 15A18, 35P30, 65Y20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-28-218, author = {Xin Huang, Zhaojun Bai and Yangfeng Su}, title = {Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {2}, pages = {218--234}, abstract = {

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method (SLAM). The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m1002}, url = {http://global-sci.org/intro/article_detail/jcm/8516.html} }
TY - JOUR T1 - Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem AU - Xin Huang, Zhaojun Bai & Yangfeng Su JO - Journal of Computational Mathematics VL - 2 SP - 218 EP - 234 PY - 2010 DA - 2010/04 SN - 28 DO - http://doi.org/10.4208/jcm.2009.10-m1002 UR - https://global-sci.org/intro/article_detail/jcm/8516.html KW - Nonlinear eigenvalue problem, Rank-one modification, Rank-one damping, Low-rank damping, Picard, Successive linear approximation method, Nonlinear Rayleigh quotient iteration, Safeguard, Global convergence. AB -

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method (SLAM). The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.

Xin Huang, Zhaojun Bai and Yangfeng Su. (2010). Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem. Journal of Computational Mathematics. 28 (2). 218-234. doi:10.4208/jcm.2009.10-m1002
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard