Cobra: Parallel path following for computing the matrix pseudospectrum

The construction of an accurate approximation of the-pseudospectrum of a matrix by means of the standard grid method is a very demanding computational task. In this paper, we describe Cobra, a domain-based method for the computation of pseudospectra that combines predictor corrector path following with a one-dimensional grid. The algorithm o€ers large and medium grain parallelism and becomes particularly attractive when we seek ®ne resolution of the pseudospectrum boundary. We implement Cobra using standard LAPACK components and show that it is more robust than the existing path following technique and faster than it and the traditional grid method. Cobra is also combined with a partial SVD algorithm to produce an e€ective parallel method for computing the matrix pseudospectrum.