Giampaolo Mele: Rational Krylov methods for linear and nonlinear eigenvalue problems

Several modern algorithms concerning the solution of eigenproblems are based on the Rational Krylov algorithm. This algorithm was firstly developed for the linear case by Axel Ruhe as a generalization of the shifted-and-inverted Arnoldi. Afterwards a few applications for the nonlinear problem were proposed. One of them is "nonlinear rational Krylov" that is a generalization of the algorithm for the nonlinear case. Another possibility is to linearize the nonlinear problem by means of Hermite-interpolations. The algorithm takes advantages in solving the linearized problem with Rational Krylov algorithm and performs an iterative linearization.