Parallel Methods for the Computation of Matrix Pseudospectra
by
Efstratios Gallopoulos
Department of Computer Engineering & Informatics, University of Patras, Patras 26500, Greece
Coauthors: C. Bekas, I. Koutis, E. Kokiopoulou, A. Sidiropoulos

Given a matrix A, the computation of its pseudospectrum, that is the locus of eigenvalues of matrices of the form A+E, for E bounded in norm by some small epsilon, is a far more expensive task than the computation of characteristics such as the condition number and the matrix spectrum. As research of the last 15 years has shown, however, the matrix pseudospectrum provides valuable information that is not included in the other indicators. So the question is how to compute it efficiently and how do we build a tool that would facilitate engineers and scientists to make such analyses? We will consider this problem from the point of view of 1) the basic computational kernels, 2) domain based information, 3) parallelism and 4) the programming environment and will provide a review of our recent efforts on this subject.

This work has been partially supported by the Greek General Secretariat for Research and Development, Project \Pi E N E \Delta 99-07

http://www.hpclab.ceid.upatras.gr

Date received: March 25, 2001