NONLINEAR RANK-ONE MODIFICATION OF THE SYMMETRIC EIGENVALUE PROBLEM

被引：21

作者：

Huang, Xin ^{[1
]}

Bai, Zhaojun ^{[2
,3
]}

Su, Yangfeng ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Univ Calif Davis, Dept Comp Sci, Davis, CA 95616 USA

[3] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 02期

关键词：

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

D O I：

10.4208/jcm.2009.10-m1002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigen-vibrations 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.

引用

页码：218 / 234

页数：17

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