Numerical Analysis Group Research Report NA-00/11

Large-scale computation of pseudospectra using ARPACK and eigs

Thomas G Wright and Lloyd N Trefethen

June 2000, 19 pages

ARPACK and its MATLAB counterpart, eigs, are software packages that calculate some eigenvalues of a large non-symmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra 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 the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000.

Key words and phrases: Arnoldi, ARPACK, eigenvalues, implicit restarting, pseudospectra

This paper is available as a 306,256 byte gzipped PostScript file.

Further information is available about the MATLAB Pseudospectra GUI mentioned in the report.