Avoiding discretization issues for infinite-dimensional eigenvalue problems

The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. In this talk, we will show that one must be extremely careful when discretizing linear and nonlinear eigenvalue problems to avoid introducing spurious eigenvalues and missing spectra. We propose a solver for general holomorphic infinite-dimensional linear and nonlinear eigenvalue problems using contour-based methods that avoids discretization issues.

This is joint work with Andrew Horning and Matthew Colbrook.