Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem

Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem

Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.10-m1002

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 218–234

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

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.

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