A survey on variational characterizations for nonlinear eigenvalue problems

Electronic Transactions on Numerical Analysis

article

Jörg Lampe¹  Heinrich Voss² 

[1] Institute of Electrical Engineering, System Theory and Mathematics, University of Applied Sciences Cologne;Institute of Mathematics, Hamburg University of Technology

关键词: nonlinear eigenvalue problem;    variational characterization;    iterative projection methods;    AMLS;    quantum dots;    viscoelastic damping;    total least-squares problems;    fluid-solid interaction;   

DOI  :  10.1553/etna_vol55s1

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

Variational principles are very powerful tools when studying self-adjoint linear operators on a Hilbert space $\mathcal H$. 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.

【 授权许可】

Unknown