A parallelizable scheme for pseudospectra computing of large matrices

The pseudospectra is a powerful tool to study the behavior of dynamic systems associated to non-normal matrices. Studies and applications have increased in the last decades, thus, its efficient computation has become of interest for the scientific community. In the large scale setting, different approaches have been proposed, some of them based on projection on Krylov subspaces. In this work we use the idea proposed by Wright and Trefethen to approximate the pseudospectra of a matrix A using a projection H-m of smaller size. Additionally, we propose a domain decomposition of the interest region into subregions which are assigned to a set of processors. Each processor calculates the minimal singular values of matrices (zI - H-m) where z = x + yi represents a point of the corresponding subregion. We conduct a numerical experimentation comparing the results with those on the literature of the topic. In all cases the proposed scheme shows a reduction in CPU time with respect to the sequential version, achieving from 41x to 101x. (C) 2013 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espa (n) over tildea, S.L.U. All rights reserved.