Large-scale computation of pseudospectra using ARPACK and eigs

ARPACK and its MATLAB counterpart, eigs, are software packages that calcula te some eigenvalues of a large nonsymmetric matrix by Arnoldi iteration wit h implicit restarts. We show that at a small additional cost, which diminis hes relatively as the matrix dimension increases, good estimates of pseudos pectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not t he eigenvalues are likely to be physically significant. Examples are presen ted for matrices with dimension up to 200,000.