Computation of Pseudospectra by Continuation

The concept of pseudospectrum was introduced by L. N. Trefethen to explain the behavior of nonnormal operators. Many phenomena (for example, hydrodynamic instability and convergence of iterative methods for linear systems) cannot be accounted for by eigenvalue analysis but are more understandable by examining the pseudospectra. The straightforward way to compute pseudospectra involves many applications of the singular value decomposition. This paper presents several fast continuation methods to calculate pseudospectra of diierent types of matrices.