A rational approximation method for the nonlinear eigenvalue problem.

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then to linearize the resulting problem. A few different schemes are proposed to solve this linear eigenvalue problem. The expanded form of the linear problem is not solved directly but it is exploited instead to extract all eigenvalues in a certain region of the complex plane. A few theoretical results are established to explain why the approach works and a few numerical experiments are described to validate it.