Chapter 60

# Nonlinefr Eigenvalue Problems

Heinrich Voss

Hamburg University of Technology

This chapter considers the nonlinear eigenvalue problem to find a parameter λ such that the linear system

$\begin{array}{cc}T\left(\lambda \right)x\text{=0}& \left(60.1\right)\end{array}$

has a nontrivial solution x, where T(·) : D → ℂn×n is a family of matrices depending on a complex parameter λD.

It generalizes the linear eigenvalue problem Ax = λx, A ∈ ℂn×n, where T(λ) = λIA, and the generalized linear eigenvalue problem where T(λ) = λBA, A, B ∈ ℂn×n.

Nonlinear eigenvalue problems T(λ)x = 0 arise in a variety of applications in science and engineering, such as the dynamic analysis of structures, vibrations of fluid-solid structures, the electronic behavior of quantum dots, and delay eigenvalue problems, to name ...

Get Handbook of Linear Algebra, 2nd Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.