Cobra: Parallel path following for computing the matrix pseudospectrum

The construction of an accurate approximation of the is an element of -pseu dospectrum of a matrix by means of the standard grid method is a very deman ding computational task. In this paper, we describe Cobra. a domain-based m ethod for the computation of pseudospectra that combines predictor correcto r path following with a one-dimensional grid. The algorithm offers large an d medium grain parallelism and becomes particularly attractive when we seek fine resolution of the pseudospectrum boundary. We implement Cobra using s tandard LAPACK components and show that it is more robust than the existing path following technique and faster than it and the traditional grid metho d. Cobra is also combined with a partial SVD algorithm to produce an effect ive parallel method for computing the matrix pseudospectrum. (C) 2001 Elsev ier Science B.V. All rights reserved.