Title: Nonlinear Eigenvalue Problems:
Computation via Contour Integration, and Transient Analysis for Delay Equations
Abstract: Nonlinear matrix eigenvalue problems exhibit fascinating structure: for example, finite dimensional problems can have infinitely many eigenvalues. Lacking a settled, general-purpose method for solving such problems, the field is at a dynamic stage of algorithmic innovation. After giving a general introduction to nonlinear eigenvalue problems, this talk will describe a new algorithm based on complex contour integration, inspired by data-driven system realization techniques from control theory. The second part of the talk will focus on a specific application: transient dynamics of solutions to delay differential equations.
Joint work with Michael Brennan, Alex Grimm, and Serkan Gugercin.