Nonlinefr Eigenvalue Problems
Hamburg University of Technology
This chapter considers the nonlinear eigenvalue problem to find a parameter λ such that the linear system
has a nontrivial solution x, where T(·) : D → ℂn×n is a family of matrices depending on a complex parameter λ ∈ D.
It generalizes the linear eigenvalue problem Ax = λx, A ∈ ℂn×n, where T(λ) = λI − A, and the generalized linear eigenvalue problem where T(λ) = λB − A, 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 ...