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

Xin Huang ,  Zhaojun Bai and Yangfeng Su

10.4208/jcm.2009.10-m1002

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

Preview Full PDF BiBTex 0 385
  • 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.

  • History

Published online: 2010-04

  • Cited by