Iterative Projection Methods for Large-Scale Nonlinear Eigenvalue Problems

In this presentation we review iterative projection methods for sparse nonlinear eigenvalue problems which have proven to be very efficient. Here the eigenvalue problem is projected to a subspace V of small dimension which yields approximate eigenpairs. If an error tolerance is not met then the search space V is expanded in an iterative way with the aim that some of the eigenvalues of the reduced matrix become good approximations to some of the wanted eigenvalues of the given large matrix. Methods of this type are the nonlinear Arnoldi method, the Jacobi–Davidson method, and the rational Krylov method.