A SURVEY ON VARIATIONAL CHARACTERIZATIONS FOR NONLINEAR EIGENVALUE PROBLEMS

被引：4
作者：
Lampe, Jorg [1 ]
Voss, Heinrich [2 ]
机构：
[1] Univ Appl Sci Cologne, Inst Elect Engn Syst Theory & Math, Cologne, Germany
[2] Hamburg Univ Technol, Inst Math, D-21071 Hamburg, Germany
来源：
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2022年 / 55卷
关键词：
nonlinear eigenvalue problem; variational characterization; iterative projection methods; AMLS; quantum dots; viscoelastic damping; total least-squares problems; fluid-solid interaction; GOVERNING ELECTRONIC STATES; JACOBI-DAVIDSON METHOD; FINITE-ELEMENT-METHOD; ILL-POSED PROBLEMS; LEAST-SQUARES; TIKHONOV REGULARIZATION; MATRIX POLYNOMIALS; VISCOELASTIC STRUCTURES; DIFFERENTIAL-EQUATIONS; SUBSTRUCTURING METHOD;
D O I：
10.1553/etna_vol55s1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Variational principles are very powerful tools when studying self-adjoint linear operators on a Hilbert space H. Bounds for eigenvalues, comparison theorems, interlacing results, and monotonicity of eigenvalues can be proved easily with these characterizations, to name just a few. In this paper we consider generalizations of these principles to families of linear, self-adjoint operators depending continuously on a scalar in a real interval.
引用
收藏
页码：1 / 75
页数：75
相关论文
共 258 条
[1]  
Abdulle A., 2015, NUMERICAL MATH ADV A, V103, P305
[2]  
Abramov Y.S., 1993, J SOVIET MATH, V64, P1278
[3]  
ABRAMOV YS, 1973, DOKL AKAD NAUK SSSR+, V212, P11
[4]  
Adcock R.J., 1877, ANALYST, V4, P183, DOI DOI 10.2307/2635777
[5]   Direct time-domain integration for exponentially damped linear method systems [J].
Adhikari, S ;
Wagner, N .
COMPUTERS & STRUCTURES, 2004, 82 (29-30) :2453-2461
[6]  
Adhikari S, 2014, STRUCTURAL DYNAMIC ANALYSIS WITH GENERALIZED DAMPING MODELS: IDENTIFICATION, P1, DOI 10.1002/9781118862971
[7]   Analysis of asymmetric nonviscously damped linear dynamic systems [J].
Adhikari, S ;
Wagner, N .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2003, 70 (06) :885-893
[8]   Iterative Methods for Eigenvalues of Viscoelastic Systems [J].
Adhikari, Sondipon ;
Pascual, Blanca .
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2011, 133 (02)
[9]   Eigenvalues of linear viscoelastic systems [J].
Adhikari, Sondipon ;
Pascual, Blanca .
JOURNAL OF SOUND AND VIBRATION, 2009, 325 (4-5) :1000-1011
[10]   NEW LOOK AT STATISTICAL-MODEL IDENTIFICATION [J].
AKAIKE, H .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1974, AC19 (06) :716-723
12345678910