Numerical Analysis: Iterative methods for nonlinear eigenvalue problems
This project involves the derivation and study algorithms for new types of nonlinear eigenvalue problems.
In many situations, a discretization of a partial differential equation and a linearization lead to the problem of computing eigenvalues of a large matrix. In contrast to this, this project involves the derivation and study algorithms for new types of eigenvalue problems which are nonlinear, thereby providing the possibility to study new recent types of physical models. The project involves development and study algorithms, theory, applications and software with the objective to reach higher accuracy and efficiency. The new algorithms are analyzed and developed with tools from numerical linear algebra and complex analysis, in particular Krylov methods and the theory for analytic functions. The algorithms are used to study specific problems in acoustics and quantum chemistry, e.g., in order to study the ground state of Bose-Enstein condensates. The convergence of one of the iterative methods is illustrated in this video.