Computing pseudospectra of polynomial eigenvalue problems: direct approach vs linearization

Abstract

Pseudospectra of polynomial eigenvalue problems (PEPs) have been investigated in recent years. In this paper, we firstly investigate the grid method, linearization method for pseudospectra of PEPs. Then, we explore a method for computing the pseudospectra of large PEPs, which is so called generalized projection method that projects to reduce the size of the problem directly using the generalized Arnoldi iteration. At last, numerical experiments and comparisons are given to illustrate the efficiency of generalized projection method and the different sensitivity of these methods.