Numerical Methods for Eigenvalue and Control Problems

Abstract

We briefly survey some of the classical methods for the numerical solution of eigenvalue problems, including methods for large scale problems. We also briefly discuss some of the basics of linear control theory, including stabilization and optimal control and show how they lead to several types of eigenvalue problems. We then discuss how these problems from control theory can be solved via classical and also nonclassical eigenvalue methods. The latter include recently developed structure preserving methods for the solution of Hamiltonian eigenvalue problems. We also demonstrate how structured eigenvalue methods can be developed for large scale and polynomial eigenvalue problems.