Computation of Pseudospectra by Spectral Dichotomy Methods in a Parallel Environment

Abstract

The standard methods for computing pseudospectra of matrices are based on the computation of the smallest singular value on each point of the domain of interest, which must be discretized beforehand. A different approach consists of determining the different regions that constitute the pseudospectrum and computing the spectral projector associated with each region. The determination of these regions and the computation of the corresponding projectors use the spectral dichotomy methods. We briefly recall these methods and propose a parallel version with performance results obtained on CRAY T3E parallel machine.