A survey on variational characterizations for nonlinear Eigenvalue problems

Publikationstyp
Journal Article
Date Issued
2021
Sprache
English
Author(s)
Lampe, Jörg  
Voß, Heinrich 
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/11302
Journal
Electronic transactions on numerical analysis  
Volume
55
Start Page
1
End Page
75
Citation
Electronic Transactions on Numerical Analysis 55 : 1-75 (2021)
Publisher DOI
10.1553/etna_vol55s1
Scopus ID
2-s2.0-85119983175
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.
Subjects
AMLS
Fluid-solid interaction
Iterative projection methods
Nonlinear eigenvalue problem
Quantum dots
Total least-squares problems
Variational characterization
Viscoelastic damping