*Title*: **A Rational Approximation Method for The Nonlinear Eigenvalue Problem**

*Abstract*: In this talk we discuss 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 apply a form of linearization. Eigenpairs of
the expanded form of this linearization are not extracted directly. Instead, its structure is exploited
to develop a scheme that allows to extract all eigenvalues in a certain region of the complex plane by
solving an eigenvalue problem of much smaller dimension. Because of its simple implementation and
the ability to work eciently in large dimensions, the presented method is appealing when solving
challenging engineering problems. A few theoretical results are established to explain why the new
approach works and numerical experiments are presented to validate the proposed algorithm.

CAM Seminar Fall 2020