Contour integration via rational Krylov for solving nonlinear eigenvalue problems

The Cauchy integral reformulation of the nonlinear eigenvalue problem A(λ)x = 0 has led to subspace methods for nonlinear eigenvalue problems, where approximations of contour integration by numerical quadrature play the role of rational filters of the subspace. We show that in some cases this filtering of the subspace by rational functions can be efficiently performed by applying a restarted rational Krylov method. We illustrate that this approach increases computational efficiency. Furthermore, locking of converged eigenvalues can in the rational Krylov method be performed in a robust way.status: publishe