A Modified Newton Method for Nonlinear Eigenvalue Problems

被引：4

作者：

Chen, Xiao-Ping ^{[1
,2
]}

Dai, Hua ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

[2] Taizhou Univ, Dept Math, Taizhou 225300, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2018年 / 8卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonlinear eigenvalue problem; smallest singular value; Newton method; quadratic convergence; SINGULAR VALUE DECOMPOSITION; LATENT VALUE-PROBLEM; MATRIX; ALGORITHMS; EQUATIONS;

D O I：

10.4208/eajam.100916.061117a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A modification to the Newton method for nonlinear eigenvalue problems is proposed and locally quadratic convergence of this algorithm is established. Numerical examples show the efficiency of the method and reduced computational cost.

引用

页码：139 / 150

页数：12

共 34 条

[1] Eigenvalues of linear viscoelastic systems [J].

Adhikari, Sondipon ;

Pascual, Blanca .

JOURNAL OF SOUND AND VIBRATION, 2009, 325 (4-5) :1000-1011

[2]

[Anonymous], 2001, LECT NOTES CONTROL I

[3]

[Anonymous], 2008, THESIS

[4]

[Anonymous], 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003

[5] NUMERICAL COMPUTATION OF AN ANALYTIC SINGULAR VALUE DECOMPOSITION OF A MATRIX VALUED FUNCTION [J].

BUNSEGERSTNER, A ;

BYERS, R ;

MEHRMANN, V ;

NICHOLS, NK .

NUMERISCHE MATHEMATIK, 1991, 60 (01) :1-39

[6] Asymptotic analysis relating spectral models in fluid-solid vibrations [J].

Conca, C ;

Osses, A ;

Planchard, J .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (03) :1020-1048

[7] ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS [J].

Dai, Hua ;

Bai, Zhong-Zhi .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2010, 28 (06) :745-766

[8] A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures [J].

Daya, EM ;

Potier-Ferry, M .

COMPUTERS & STRUCTURES, 2001, 79 (05) :533-541

[9] NONEQUIVALENCE DEFLATION FOR THE SOLUTION OF MATRIX LATENT VALUE-PROBLEMS [J].

GUO, JS ;

LIN, WW ;

WANG, CS .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 231 :15-45

[10] Numerical simulation of three dimensional pyramid quantum dot [J].

Hwang, TM ;

Lin, WW ;

Wang, WC ;

Wang, WC .

JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 196 (01) :208-232

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