Numerical Analysis for Nonlinear Eigenvalue Problems

D. Bindel (CS, Cornell)

Nonlinear eigenvalue problems occur naturally when looking at differential equation models that include damping, radiation, or delay effects. Such problems also arise when we reduce a linear eigenvalue problem, as occurs when we rewrite a PDE eigenvalue problem in terms of a boundary integral equation. In each of these cases, we are interested in studying the values of z for which the meromorphic matrix-valued function A(z) is singular (or nearly singular) as a way to study linearized system dynamics. In this talk, I describe extensions of some standard perturbation results and bounds to the case of nonlinear eigenvalue problems, and apply these results to error estimates for computing resonances and eigenvalues of Schroedinger operators.